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.