I always enjoy breaking the rules in normal video games, it's one of the things that keeps me playing them. If I couldn't cheat using in-game cheats, or a device like CodeBreaker or Action Replay or GameShark, I don't think I'd still be as big of a gamer as I am today.
Mind you, I'm getting older and it's getting harder to afford games, so I do tend to almost soley stick to games I'm either confident I can play (like Zelda) or games I already know have cheats in them or for them. It's one of the reasons I've become more interested in PC games again, because most have in-game cheats (or at least trainers) or mods or hacks or other fun stuff.
As someone else has pointed out, it seems many developers/programmers are shying away from in-game cheats, and I find it sad. I don't play games for silly "Achievements" or for some ridiculous sense of "challenge". I play video games because I want to relax and entertain myself. Games with good storylines and plot keep me going through it to the end, regardless of cheating. Likewise, games that are just fun as hell to play (like Devil May Cry or Kirby) keep me going because they're fun. I don't care if I'm invincible or not, so long as I can have lots of fun and don't have to worry about dying every five seconds (like some games do...).
I think that's what mostly put me off of the original Xbox. Very few games I wanted, and the ones I did want had nothing interesting in the vein of in-game cheats or a 'game enhancer'. There was nothing there to keep me coming back if I sucked at a game. In the times when money is hard to come by, I have to be absolutely sure I'm gonna enjoy something I buy. Without that net below to catch me if I fall, I'm not gonna really enjoy it. Why buy an expensive console only to regret it? I made that mistake with the Dreamcast, which had some great games, but not nearly enough of them, and I spent so much money on the console I only could afford a handful of games afterwards.
EDIT: I should point out that I dispise online games, so people don't have to worry about me cheating on those. Not that I would anyways. Cheating when you're screwing around in a single player game is fine, but when it hurts others, it's just fucked up and unfair. I mean, most online games are rather unfair already, no sense making it worse for others.