Backdooring

I like to backdoor with Yasuo, because late game he can do really devastating auto-attack damage, and has enough survivability to take some damage and escape for an entire team. With bloodthirster I've even killed an inhibitor turret without losing more than about 10% of my actual health, and that's with no friendly minion wave to take any of the turret shots for me.

To be fair, I think it had some damage on it before I got to it, but it was still an exciting play for me.

I also like to backdoor with Caitlyn, just because she gets similarly insane auto-attack damage the way I build her. Though in her case she either needs a tank to soak some tower hits, or she just backdoors already exposed inhibitors.

with 600+ stacks and triforce.

I've backdoored at least 3 Nexus's with Nidalee. Usually with IBG-> Shiv/Botrk -> tank or just Triforce -> tank.

A couple of them were incredibly close too with them pushing our base. Only proper stutter stepping and maximizing sheen procs got me the win.

The godyr

I don´t really like it as a strategy, as it´s kinda low risk - high reward if executed well (4-1splitpush). best Champ to do it though is Tryn hands down: fast push, god in 1v1/2 and really good in escaping aswell later on.

For sure my favorite split-pusher/"backdoorer" has to be the one and only His passive makes him extremely OP for taking towers/inhibs/nexus' plus if built right can out put tons of damage while taking little thus providing a better chance at a badass escape or even taking the objective before they can kill you

Commander Olaf, at your service. I've had some awesome games where I run Olaf with TP and Ghost. Deep jungle wards, TP in, ghost your way through to base, and BAM. I've done the same with Malphite. It's something about the AS/AD steroids (respectively) that make them so much fun to take objectives with.

Backdooring, and by extension splitpushing, is a highly overrated strategy in my opinion. Without massive early leads, it's actually quite difficult to assemble a four man squad that can adequately support the splitpusher and deny both teamfights and objectives from the enemy team. There are certainly instances where using a champion like Zed to create side lane pressure is helpful, but the SoloQ style of "I am Jax. This turret killed my father. I shall never leave this lane until it is dead" is pretty stupid.