I have been playing Blitzcrank for a while now and he's one of the most fun champions to play. I play Blitz as an supportive tank who gets kills for your teammates with his grabs.
He's also good at solo laning, but nontheless u have the most fun when u are in lane with someone else.
This is my first build and I hope u will like it.

Pros:
-Great laning partner
-Usefull in teamfights
-Can do solid dmg for an tank
-great disabler with his area silence
-He's very fast for an big guy
-great for clearing minion waves

Cons:
-lacks finishing power
-Mana dependent ealy game
-Is somewhat weak end-game compared to the beginning of the game.

Main items:
When playing Blitz mine core build consists of Frozen Heart and Shurelya's Battlesong for a lot of CD. This makes u able to spamm all of his skills.
This is expecially usefull with his Static Field (with about 20 sec CD)since it can wipe out entire waves of creeps. And it alows u to spamm your Overdrive skill, getting u 450+ movement speed all the time.
And if u combine Overdrive, Mobility Boots, and the active of Shurelya's Battlesong then u get 550 movement speed for 3 seconds =D , great for running away.

Boots:
like most tank-like champions your choice of boots will depend on the enemy team.
If there is a lot of CC take Mercury's Treads, otherwise Boots of Swiftnessor Mobility Boots.

Optional Items:
Warmog's Armor and/or Force of Nature if the enemy team has a lot of AP
Thornmail if your opponent has a lot of AD
Trinity Force is a great all-round item but not rly something I prefer.
Guardian Angel What can I say, an revive is always welcome

Going with AP?:
If u like to play Blitz with some AP (late game) then take Rabadon's Deathcap and Archangel's Staff, This way your ult can nuke all their carries in teamfights.
Instead of Archangel's Staff u can take Lich Bane for awsome dmg with your Power Fist

Beginning with no runes?:
At the beginning of the game I always buy the Regrowth Pendant because I have enough mana regen from my runes. If u dont have the mana regen runes, I suggest u start with an Sapphire Crystal and go for the Glacial Shroud.

Spells? Take Clarity! Clarity is great for Blitz. You always want to have some mana for grabs at any time, and since you want go get kills/assists while you are laning it's important that u have enough mana for grabs.
Besides mana for skills it can give your passive an extra shield boost.

as an second spell I take Flash. If u flash away and use Overdrive and Reverie's active u can get away very easy.

Having spells like Ignite or Cleanse are also very usefull. Ignite for the extra dmg and cleanse for escaping.

having Heal is not so great compared to clarity since clarity indirectly heals because of the passive.

One spell I do not advice is your Teleport spell, when walking with 450+ movement speed u can walk from one lane to the other very fast. making teleport not so usefull compared to the other options.

--Blitzcranks Static Field is an multi-fuctional skill that can be used to trick your opponent as followed:
If u are in lane near your turret while your opponent(s) are behind their minions u can't grab them. First weaken the minions ,then use your Static Field to whipe the minion-wave in an instant.
Now that the minions are gone, u can quickly grab them in your turret.

--When u are (almost death and) running towards your tower while being chased.
If you are within the range of the turret, use your Rocket Grab to pull the greedy bastard and use your Power Fist. If done right the turret should hit the enemy 2-3 times before he dies.

I think some people agree with me when I say that Blitzcrank is an champion that takes a while to master and has a lot of different item builds. Just find your own way of playing Blitz and before u know it u can win while saying: ALL UR BASE ARE BELONG TO US.
http://www.youtube.com/watch?v=qItugh-fFgg