If you are lit on fire by a molotov or just a car explosion fire, jump non-stop, this will prevent the fire to do any damage to you.
Some people don't know this, but you can actually rob the chillidog stands.
To the new guys: To actually break the vault door of the bank, you don't always need to crack it, if you find or purchase a C4 explosive from the ammunition you can actually place that on the vault door to explode it open, making it much easier to rob the place.
If you're a criminal, you can do $cop to print out the name of the nearest cop to you. Then just do /loc (cops id) to find where and especially how far he is from you.
If you're a cop and a criminal is running away from you unarmed, you can't shoot him, but what you can do is try and ram him, to stop him. Just remember not to kill the guy.
A normal bicycle is quite a decent getaway vehicle in some situations. The main reason for this is the bicycles ability to jump, making you very hard to chase by vehicle, because you can jump over various walls, which cops can't follow with normal vehicles. Just watch out, if they shoot you, you will tumble off the bicycle.
When robbing an ATM, you don't always have to wait for the full animation, you can actually destroy the atm by just shooting it, but do remember this will give less money then fully robbing it. Good to do in a pinch.
If you're a cop and chasing a criminal on foot and he tries to enter a vehicle, whilst the entering animation is playing (opening door, sitting in) you can actually press N to cuff them in the position where they enter the vehicle, so don't try and carjack them out of it, just cuff them straight away.
There's also a thing called lag pitting in SA-MP. Here's a quick video explaining it and showcasing it: