I noticed there weren't any offtank Heimer builds out there, so I decided to make one. It sounds stupid, but it isn't. I'd like to present to you my way of Heimerdinging. Or, should I say, Heimundyinging. Have a nice read!
By the way, I made use of the acronym system in this guide. Hover your mouse over yellow words to pop up that yellow-toned square with more information or a definition on something.

Please actually read the build before voting, and test it out before saying it sucks. Also, when you downvote it, please provide feedback so I can fix what you found wrong about this build.

January 11th, 2011 - Build published.
Some hours after the build was published - Added "Early Game", "Mid Game" and "Late Game" sections.

January 12th, 2011
Remade 'Items' section.

February 6th, 2011
Added 'Why should anyone build Heimer this way?' section.
Added 'Patch Notes Review' section.
Added 'Pure Tank' build.

February 24th, 2011
Removed Clarity from Spells.

March 22nd, 2011
Added icons on Items section (requested).

March 30th, 2011
Removed Rylai's Scepter Rylai's Scepter from item builds that contained it because Heimer's turrets no longer apply the slow or when I tested it, it was a bug.

April 1st, 2011
Added "Unbeatable Turret Destroyer" item build to Items section. This build helps you escape ganks and backdoor better. And lol no, this isn't an April Fools joke.

April 23rd, 2011
Added "Skill Order" section.

April 24th, 2011
Updated "Runes" section.

April 28th, 2011
Remade "Pros and Cons", "Items" and "Skill Order" sections. Some of them have also been renamed.

August 22nd, 2011
Fixed the most stupid bug ever (everything in the guide was showing 4x).
Removed Aegis of the Legion

To analyze this situation, Ill get various factors of gameplay that both builds feel when playing, and then rate both builds in Utility, Damage, Pushing Stability/Survivability and Pushing Power/Speed, from A+ to F.

Offtank Heimerdinger

Being beefy allows you to stay near your enemies means Grenades are easier to hit. Hitting more Grenades means youll be constantly applying AoE CC to your enemies, giving you more utility (which is one of Heimerdingers main opacity problems people that dont play Heimerdinger or rarely play with a good Heimerdinger constantly ask themselves what does Heimerdinger do?).
Being beefy allows you to stay next to your turrets, and that grabs the distraction from them to you, making them a reliable source of damage, even in combat, giving him better actual damage on his turrets.
Being beefy and having your turrets allows you to win maybe even a 1v3 (through strategic positioning) depending on the enemy champions that decide to gank you, giving you better pushing stability.
Being beefy allows Heimerdinger to tank turrets for a good duration, giving him better pushing power.

Not getting much AP due to the focus on survivability items makes his abilities not that strong, weakening his overall damage.
Not getting much AP due to the focus on survivability items weakens his pushing power.

Utility: B
Damage: C+
Pushing Stability/Survivability: A
Pushing Power/Speed: B+

Overall Rating: B+

AP Heimerdinger

Focusing on AP gives Heimerdinger a great boost to his skills. Rockets become a dangerous 3/5 person nuke, Grenades do tons of damage when they hit, and turrets do a great amount of damage while theyre up.
Focusing on AP makes Turrets a lot stronger, increasing pushing power/speed greatly.

Not getting much survivability due to the focus on AP items makes Heimerdinger too squishy, and being squishy and a desirable target makes Heimerdinger stay away from the core of the battle, making his Grenades harder to hit and making his turrets last less, or maybe even harder to place. This doesnt mean Grenades are never going to be hit or Turrets are never going to stay up to deal significant damage, but its hard to happen.
Not getting much survivability due to the focus on AP makes him easier to stop from pushing, lowering his pushing stability.

Utility: C
Damage: A
Pushing Stability/Survivability: C-
Pushing Power/Speed: A+

Overall rating: B+

Basically, both builds have their pros and cons. While AP Heimerdinger has its highs and lows, Offtank Heimerdinger doesnt have highs or lows, it stays in the middle.

Teleport and Ghost are pretty good for this build.

Teleport is pretty much a MUST on Heimerdinger, since he's a great pusher and that's something you can't waste. Ghost will improve your juking a lot.

Exhaust and Flash are also good and can replace one of the other two.

(These are only suggestions, you don't HAAAVE to buy them)

Magic Penetration Marks because they're so good.
Flat Mana Regeneration per 5 Seals to satisfy your early mana needs.
Ability Power per level Glyphs and Quintessences (or flat HP Quints to make your early game better) to give you some extra AP since this build focuses harder on survivability. You can also go for MR over level Glyphs for a boost in survivability vs. magic damage dealers.

21 on Utility is concrete, since the Utility tree is awesome for you. More mana regeneration, lower cooldowns...

Defensive (recommended for beginners)

0/9/21 - 9 on defense (3 on Hardiness, 3 on Resistance and 3 on Strength of Spirit) gives you some armor, MR and health regeneration per 5.

Makes your early game much safer and gives you some HP regeneration per 5.

Offensive

9/0/21 - 9 on offense, like shown up there, gives you one more set of AP glyphs, minimal CDR you won't miss, and some helpful % magic penetration.

Makes your damage better overall.

Youre building this beefy mainly because of your turrets, so max your turrets first, obviously.
Maxing Rocket first improves your deadliness in teamfights, but lowers your utility in and out of one.
Maxing Grenade first improves your utility in teamfights, but lowers your damage in one.
Now since youre building tanky, what are you able to do? Stay close to your enemies. And what is easier to do when youre close to your enemies? Hit Grenades. But whats also easy to do when youre close to your enemies? Hit 5 people with Rockets.
Leveling Grenade lowers its CD (making you able to spam it), leveling Rocket increases its damage.
Rockets are harder to hit in lane, while Grenades are hard to hit anywhere (but are easier to hit when you're closer to the enemy)
It's up to you, but one of the reasons youre building as Offtank Heimerdinger is to apply AoE stuns and leveling Grenade first allows you to spam it more.
But in the end, it doesnt make much of a difference since Heimerdinger gets to level 18 so quickly.


Note! If you choose Rockets first, your Early Game will be much better. If you're being countered early (i.e. by Caitlyn), I suggest you max Rockets before any other skill.

-> ->
/ (when there is too much CC in the enemy team)
-> (replaceable when the enemy team doesnt deal enough Physical Damage, but this is a rare occasion - read Replacements)
Catalyst the Protector -> (replaceable when the enemy team doesn't deal enough Magic Damage or doesn't have enough CC, but this is a rare occasion - read Replacements)
Catalyst the Protector -> (extremely situationally replaceable)
(irreplaceable)

Stats:
HP: 2705 (+1005)
Effective Health (EHP): 5951 (+3477.5)
Physical Damage EHP: 7033 (+4296)
Magical Damage EHP: 4869 (+2659)
Ability Power: 535.99 (+535.99)
Armor: 160 (+99)
Magic Resist: 80 (+50)

Replacements

can be replaced by when the enemy team lacks Physical Damage and has excessive CC and you are going to use the active effectively;
can be replaced by when the enemy team lacks Physical Damage;
can be replaced by if you find it a more solid choice and are going to use the active effectively;
can be replaced by if the enemy team lacks Magic Damage and you are going to use the active effectively;
can be replaced by if the enemy team has way too much CC and you are going to use the active effectively;
or Frozen Heart can be replaced by , or to boost your pushing security;
can be replaced when the situation requires you to stay with both and but get more of a stat from another item, you can replace it with any of the items said above, but be careful with the decision. Replacing it with an item you'd get over the other ones is rarely more effective than not replacing it. There could be many reasons, such as lack of gold or the serious need for or .
Also: You might want to get an early Philosopher's Stone and/or Kage's Lucky Pick and sell it/them later.

Heimer is a really good farmer and you'll probably finish your 6 items really fast. So, after you're finished, always get Elixirs whenever you can!

During the early phase of the game, you must play very defensively. Although Heimerdinger is a good farmer and pusher, you should dedicate this phase to just farm and only try to kill your enemies only when they come for you. Use your grenades to blind/stun them and spam your rockets if they try to attack you, and stay around your turrets to be constantly dealing damage while they chase you. You need to always hit your grenades if they do, since Heimerdinger is very squishy at the start of the game. Do not play aggressively, harass your enemies when they try to attack minions or your turrets, and also help your lane partner (if you have one) on farming. DO NOT push too far until Level 6, when you can go a bit ahead of the river and start to attempt to drop your enemy's turret, always leaving a turret behind to help you on escaping ganks (check Turret Placement section).
If your (big) turret suffers damage, stand near it to make use of your passive - you'll be healing it.

During the mid phase of the game, you should stay with your team most of the time, and occasionally push when you have time to or they want you to and defend when you have to. Set a turret up wherever you go - a fight can break out anytime!
Also, you should ward the map for your team all the time. Usual spots are the river spots around mid, the area in front of Baron and the area in front of Dragon. Also get Dragon all the time!
Also, at this phase of the game, you'll be able to 1v1 about anyone (except the tank) in the enemy team once you have Archangel's Staff, Boots, Banshee's Veil and Glacial Shroud.

During the late phase of the game, you should group up with your team and do the final push or push alone while your team distracts your enemies, with the area around you fully warded and turrets trategically placed (check Turret Placement). You will probably be your team's main pusher, so yeah... Push. But don't be reckless at all! Don't push when your team needs you somewheere else. At this point, you'll be losing your 1v1 awesomeness, but through juking you can still kill even the enemy carry.

As Heimerdinger, correct turret placement is crucial! Check these screenshots.
Also, some of these (mainly the ones marked with "offensive turrets") are only for the early phase of the game, to zone out or harass your enemies. The rest works anytime, to push safely and such. Also, it's not like you have to place your turrets to push during the early game, since the current way to do it is to not push.

Side Lanes

Mid Lane

Any lane

Reason number one: Heimer gains a lot of presence in teamfights this way. Even though "Heimerdinger shouldn't be at the heart of the battle", this allows the summoner to play in a less... risky way. With 40% CDR, you will be able to frequently throw Grenades, that, if hit correctly, will stun AND blind the target. And grenades are much easier to hit from nearby. In patch 1.00.109, they were made easier to hit when you use your ultimate, however being close to the target still makes the stun a lot more accurate. And your Rockets, in .109, have also been improved when you use your ultimate. With the EHP this build provides, you'll be able to throw at least 4~5 grenades and 20~25 rockets in a teamfight where you're the second priority. And your turrets will keep attacking.
Most Heimerdingers after 30:00 simply fade away from the game and become tower defenders/stealthy pushers/pokers because they're scared. With this build, you are much more than that and can carry your team.

Reason number two: Pushing becomes a lot better and safer. You can backdoor (you'll tank that tower), and the enemy team needs a 4+ man gank to stop you from pushing. Pff, dat Ashe comes to try to stop you from pushing? Haha, that dirty ape better get back.

1.0.0.109

* H28G Evolution Turret
o Improved Turret AI so they will prioritize attacking Champions that attack Heimerdinger
When they said "AI improvements" I thought they would make it so turrets actually finished minions down until the last hit (which they still don't do), also so they didn't stop attacking suddenly, and so that they also prioritized turrets when there were enemy minions nearby. But all they did was this. It's still a lot better, though. ^-^

o Turrets now work on an ammo system (25 second ammo cooldown)
You can now drop a tower REALLY fast, but I feel like the cooldown is longer now. And that isn't really helpful... but this was still an awesome buff.
o 1 second placement cooldown
o Levelup progression changed:
+ Rank 2 - places green turrets
+ Rank 3 - places 2 turrets
+ Rank 4 - +150 Health
+ Rank 5 - places red turrets
Nerf. I didn't like this. Being able to place 2 turrets at Level 3 was wonderful. Now your laning phase is less safe until level 5, unless you use your only turret to stay in the bush.

o Fixed a bug where Upgraded!!! turrets would stop firing resistance piercing and area-effect shots
Thank god.
o Turrets now gain 15 health per Heimerdinger level down from 21
Too bad! Now your turrets are easier to disable.
o Turret magic resistance increased to 80 from 60
Great.
o Tooltip now references 'turrets' rather than 'towers.'
* Upgrade!!!
o Now increases number of Hextech Micro Rockets to 5 while active
o Now increases missile speed on Ch-1 Concussion Grenade to 1000 from 750 while active
WONDERFUL buff, makes your grenades A LOT easier to hit efficiently, and your Hextech Micro Rockets are an even bigger threat.
* Fixed a bug where Techmaturgical Repair Bots provided less health regeneration than stated


Heimer is A LOT better since this patch, but experienced Heimer players might end up feeling a bit crippled due to some minor changes.

1.0.0.111
Glacial Shroud CDR down to 15%; Frozen Heart CDR down to 20%. However, masteries + ultimate passive + 20% = 40%. No problem for us here! ^-^

Don't have much to say anymore, I guess. I'll constantly update this guide depending on how the game changes, and maybe post some videos and instructions on tactical play.