I have a Tau sniper I want to put on a rocky out-cliff, that would require using a non-standard base (a larger one). Is that allowed in the rules? Would it fly in a casual game?
It's a grey area, but it's preferred that models be played with the bases provided with them with some exceptions for scenic bases. Generally as long as you haven't modeled for a clear advantage(such as using a base that's 9" tall) most players will be OK with it. To be on the safe side, you should have a standard based guy to swap in for the scenic base model it it ever appears your custom base would have an effect on the game.
There was an issue a few years back at a GW sponsored GT where a Demon player who won the tournament used smaller than standard bases for his Bloodcrushers. It was felt that this gave his particular army an unfair advantage due to some of that codex's unique rules. As a result, most tournaments will have a policy like this one from the Nova Open:
Most players I know will try to conform to the big tournament guidelines. Of course, I play with a fairly competitive group that hits a few big GT's every year.