Hello I'm Profound Pony, Heimerdinger main. I have 190k Exp and level 7 mastery on Heimerdinger. I also have a 67% winrate in ranked with tha d0nger. Heimer is my absolute favorite champion. He is an amazing champion that can go almost anywhere and fit in any team. From full utility with crazy slows and huge stuns, to ****ing deleting carries instantly, heimer does it all.

Pros
+High Utility
+Crazy, unexpected burst
+High Sustained Damage
+Most don't know how to play against him
+Able to 2v1, sometimes 3v1 without having insane mechanics
+High range on E and W
+Fits in most team comps
+Can solo drag and duo baron easily
+Scales well
+Pushes lane hard
+So. Much. Fun
Cons
-Natural squishiness
-Low mobility
-Relies heavily on having turrets pre-placed for max damage
-Without your turrets you will probably die and do nothing
-Needs to protect turrets (Get the point?)
-Stun can be hard to hit perfectly

Flash is a god-tier spell and is needed on 90% of champs, heimer is no different. More mobility is gr8
Ignite is generally nice in the midlane (and even the toplane) for some early kill pressure.
Teleport is an option toplane so you can join your team at a moments notice, but I just don't find teleporting in as a Heimerdinger with no turrets set up is very effective. Personal preference though.
Ghost is totally viable instead of flash to help kite in your turrets, I just like flash more because walls n stuff.
Exhaust is nice against champs that can one-shot you, or on champs that you need to slow the hell down so your turret beams hit them.

Toplane Heimerdinger
In the toplane, Heimerdinger should generally be played as an AP off-tank split pusher.
Generally, ignite is better than teleport because teleporting in as a Heimerdinger just isn't very effective.
Banner of Command is a great item in the toplane, especially if you're against a Ryze or Swain as you can just shove to the inhibitor turret and most people won't even bother to try and stop you until it's too late.
Toplane is also more prone to ganks because the lane is longer, giving you more opportunities for double kills :-)
I think Heimerdinger is a VERY strong toplane bully, and a great counter for champions like Darius, Nasus and Garen.

Midlane Heimerdinger
I really prefer Heimerdinger in the midlane because you have a lot of kill pressure and can attempt to snowball the game easier than being in the toplane
Why? If you get a kill in the toplane, you really can't capitalize as much on it, other than taking the tower. In the midlane, if you kill your opponent you can take the tower, force a dragon, and even roam without having to walk forever.

Heimerdinger is one of the best laning champions in the game. He has excellent tower siege, holds, and good kill potential. Heimer also is easy to farm with, because his turrets (usually) aggro whatever you're hitting.
HOW TO PLACE THA TURRETS
There are many ways you can place turrets, two of the usual, safe ones are
and
If you're fighting, just place turrets as close to the action as you can, without them getting hit by AOE damage (don't drop one on a Cinderhulk Hecarim

How to all-in
Heimerdinger is a weird champ when it comes to all in's. Usually, let the wave push naturally with your turrets until your enemy is under tower. If you have Luden's Tempest, wait until it is at 100 stacks, and make sure Thunderlord's Decree is available as well. Your combo is going to be E+R+W, autoattacks + Ignite. If you hit everything, this can completely destroy your enemy laner from well over half health.

How to turn ganks into double kills
Because Heimerdinger pushes waves so easily and naturally, he is often targetted by the enemy jungler.
You're going to need to ward as much as you can so you get a little heads up that it's about to go down. Stand in a way that makes both the enemy laner and jungler walk all the way through your turrets zones. When one or both are close, or on top of you, use your E to stun one, ult + Q on top of them, and W + Ignite the lowest one. Flash to avoid damage and then ctrl+6 when they both die :-)

If you're unexperienced with Heimerdinger, teamfighting is, by far, going to be the hardest thing to do.
Teamfighting is so different from laning for this champion.
If it's midgame, and your damage isn't crazy yet, just ult your Q and drop it on the enemies heads, put as many turrets down as you can, and try to chunk the squishiest one with E+W.
Only ult your W if you're positive you can hit it, and that it will kill. It's a huge ability that, if you miss, does absolutely nothing except embarrass you.
If it's late game, and your damage is pretty high, and your confident that you can hit abilities, aim to kill squishies. There is nothing more satisfying than landing an E and an ulted W on the enemy Ashe to drop her health 100-0.
If it's late game and you're not sure you can hit a nice stun, or the enemy team has a great frontline and/or super mobile champs, just ult Q and drop it.

If you're not almost certain your ult W will land, Just. Use. Your. Q.
Reliable damage is so much better than taking huge risks for no reason :-)

Heimerdinger has excellent siege, anti-siege, and overall objective control.
Sieging
With or without Banner of Command, Heimerdinger is an incredible sieger.
Wait until the turret is aggro on a cannon or melee minion, and just drop your turrets. three turrets and/or an ulted turret absolutely MELT turrets and inhibs.
If you have Banner of Command it gets ridiculous. No one will be able to solo anti-siege you.

Anti-Siege
Enemy team storming your nexus? Drop three turrets and an ulted one and they will back off reall quick, or take massive damage.

Objective control
Never forget that Heimerdinger can solo dragon without even entering the pit. Just drop your turrets from behind the wall and it's all good.
At level 11, if you have a carry jungler Master Yi, Xin Zhao, etc. you can duo baron! Drop turrets + ult and go 4 it.

will add more ish when I want :-)
Update log
7/17/2016 added pictures and toplane build
7/20/2016 added some matchups and support build