Ad carry comes to mind first. You could take down towers pretty quickly too.

Actually, cho would work. He can decimate waves, does plenty of tower damage, and is tanky enough to walk away once he is noticed. In fact, most people don't bother with a full size cho solo anyway and splitting their team between you and the rest of your team is a bad idea.

Ive had relative success with using Shaco after jungling to split push. Since he is played as an Assassin he isnt that missed in team fights.Unless Im the only one able to get to the squishies in the back. His boxes placed either along the lane or in key entry points from jungle allow map awareness much like Teemo's mushrooms. Add in his deceive that jumps almost any wall and an invis, he is almost impossible to catch. Usually I run Smite and Exhaust for summoner spells and I can 1v1 almost anyone if I have been getting good ganks early game. This is just my 2 cents though, considering you rarely see Shaco anymore.

Edit: Forgot to mention the fact that his Clone doubles your attack speed, takes the turret hits first and is on a pretty small cooldown. Also, you can place a box right near the turret, it will either take a hit for you, or with enough time attack the turret adding to the speed in taking it down.

I have been playing Wukong as Solo Top. It seems to work great til, you get a bad team who doesn't call mia.... then again thats for everything.

Wukong, Yi, and Sivir are amazing from what I have seen.

4 tiamat parrley

singed can push but dont think he will take a tower down before enemy comes.

Malzahar can clear minions up quickly with skills and mana still available to deal with lane rivals.

Ganking is not his strong point but you CAN go to other lanes, leave malefic visions and a Null Zone behind and quickly get back your duty.

Tryndamere is a good solo pusher because of his attack speed and spin ability (escape).
Jax eats turrets for breakfast. For added lulz, get him a Guinsoo's Rageblade.
Yi is a classic backdoor character.
Cho'Gath eats minion waves, but he isn't the greatest for actually damaging the turret. However, if he's at full ult stacks, there's not much enemies can do about him if you're using him to backdoor.
Warwick can take out turrets pretty well because of his W's attack speed boost.
Malzahar and Karthus can take out minions with ease, but they suck at taking down turrets.
To backdoor as Singed, the trick is to use your Q gas to kill enemy minion waves before they can give their turret backup, then go autoattack the turret with your minions. Not to mention he's Singed- no one wants to go deal with Singed...
I would list some more AD carries, but really, any AD carry can backdoor/split push like a boss.

In my opinion, if you want to push a lane or back door in general, late-game AD shaco would be a really good choice. If you have tri force and 2 phantoms, pushing a lane is literally like 10 seconds. On another note, Shaco also has really great escape abilities with a build in stealth/flash and JITB's to cover up his escape. Sure, you'd have to be really late-game to do this, but shaco is a really good choice. Building like this is up to you.

as sivir i can shred an entire minions wave with 2 abilities... boomerang and Ricochet
with minion waves falling so quickly u can push a lane stupidly quickly, ur also getting farm and if u pop her ult on the turret they fall to sivir quickly

Nidalee is actually very strong at split-pushing, especially when you include a rageblade in your build.