1. save states
with save states, you can press a button to take a snapshot of the state of the game, then instantly revert the game to that state with the press of another button. this enables you to do several things. if you are trying something that might not work (using a rare item, for instance), save the state just before trying it. you can reload the state if it doesn't work. another possibility is manipulation of random events. if you don't get the result you want, reload the state. finally, if there's just a tough part of the game, you can get as many tries as you want without ever losing a life.
note: some games like Half Life have save states built in.
2. save state hacking
by necessity, a save stack includes a list of all the items in your inventory, or else has flags that tell the game whether or not you have an item. it also includes information like your characters' statistics, amount of money, etc. if you dig up the save state file and open it in a hexadecimal editor, you just might be able to alter the save state in a favorable way. this is not a very exciting way to cheat, though. oh, look, i have a million hit points! oh, look, the game crashed! this tends to happen if you aren't careful.
3. fast forward
with a fast forward button, you can skip through tedious dialogue, or run around in the field getting level-ups at super speed. if you are guaranteed to win the battle, why micro-manage it at normal speed? just hold down "attack" and fast-forward through it! this isn't really cheating, but it does make some things easier.
4. enlisting a computer for help
in deterministic games like Chess or Go, a fast computer with the proper algorithm is often a better player than most humans. this means you can play such a game online and simply enter your opponent's moves into your local game as your own moves. then when the computer makes a move, you make that move in the online game. it's fun to go on a rampage with the grandmaster-level Chessmaster 9000 program and beat the snot out of unsuspecting online denizens. of course, if you're feeling guilty, you can intentionally lose to even things out.
no longer will we live by the arbitrary rules of computer games! it's the age of participation, bitches!