There's more than just AD that can split push. I'm going to try and name some champions who haven't been listed yet.
My first split pusher was this guy:
He can shove a lane with just tiamat and 1 use of his Q. He's not mobile but he can really push a lane and his damage output is quite good for taking down towers.
He can really do a significant amount of damage on a tower when left alone... And his Q actually works on the tower.
Should be first on anyone's list for split pushing prowess.
Her ultimate is all about wiping out minion waves with little to no effort. She can't really take out towers but keep the waves off of her own towers.
Can take out up to 5 of the minion wave when he gets enough AD using 1 Q ability, but what he really excels at is backdooring the turrets.
Late game when he gets enough AP all he has to do is cast E on anything that isn't a super minion and let his space AIDs wreck havok on the wave. Then make his way out to another lane and repeat the process.
If Udyr maxes out his Tiger, Turtle and Phoenix stances he has all the tools he needs to split push. Phoenix for the wave clear, Tiger for the tower take downs and Turtle for tanking/sustaining. And he can get his aspect of the monkey to 3 stacks and has some pretty good speed through that.
Is actually not a great split pusher. He is item reliant. If you build statik shiv and luden's echo he can push out waves but without this he is not very good at it.
Can't forget about the spell spammer. His main purpose is to spam spells and clear out massive waves of minions. Oh and he's tanky to boot.
Vladimir is just like Malzahar and Ryze. Stick him in the middle of a massive minion wave for a good 5-8 seconds and the whole wave will be gone. And he doesn't use mana and with a hextech revolver can actually heal off minion waves by doing this.
Lastly is Rek'sai. Her Queen's wrath has some decent AOE wave clear. But her ultimate is where it's at. She can push top lane, see a gank incoming and head bot lane and shove out there too. She may even take out a tower before the enemy team can make their way back to where she is. And when they do she can just teleport right back to top lane on one of her tunnels or a ward and take that tower too.