Today we're talking about infinite combos. In a game, you can sometimes find ways to shift your resources around so that you end up with more than you started with. At which point you can keep doing it, and keep doing it, and generate massive amounts of resources. In real life these examples are less common because almost inevitably you encounter negative feedback along the way. Here, let me give you an example.
In the game Morrowind you can practice alchemy. Take ingredients A and B, mix them together, and make a potion. Pretty much the standard fare for modern fantasy games. The trouble comes with the way stores work. If you sell your frost salts to an armorsmith you'll never see them again. If you sell them to an alchemist who already has one in stock, his stock will permanently go up by one. So buy both salts back from him; then close and reopen his window; he'll have two more salts for you to buy. As many times as you like. Or keep selling them back to build up a real proper inventory. It's a real easy way to get otherwise hard to acquire reagents.
If you take two foodstuffs and mix them together, you get a potion of restore fatigue. Not terribly useful, except that it sells for significantly more than the ingredients cost. But if you use the store exploit I mentioned above, you can keep buying reagents, keep selling potions, and get essentially infinite money and stockpiles of powerful potions and rare reagents.
Understandably this does bad things for game balance. On the other hand, Morrowind is a strictly single player game, so that's less important.
I'm going to define some terms quick.
Bug: A bug is anytime when a game does something it wasn't designed to do. This just indicates that the game isn't working properly. For example, in Diablo II if you stood in the bottom corner of Atma's tavern and dropped an item, it would land outside the wall even if you were inside. Usually bugs occur in a computer game, but not always. They've printed Magic cards that play havoc with the rules before. (You used to be able to give judges headaches with Opalescence and Humility. They've since worked it out.)
Exploit: An exploit is anytime you can use a convocation of mechanics or a bug for personal gain. That Atma's tavern bug? I remember it because people could use it to scam people in trades (we each drop an item, then we run around to pick up the other persons. Go stand in the corner so you'll be sure I can't get to yours before you get to mine.) When it's just an oddity in the game, it's a bug. When you can do something with it, like scam other players or make infinite potions, it's an exploit.
Hack: A hack is essentially a way of cheating at the game. Wallhack in counterstrike or loaded dice in back alley craps. What differentiates a hack from an exploit is that in an exploit you're using the rules of the game as they're laid out, with a hack you're changing those rules. To continue the craps example, on your basic come/don't come bet you've got about a 1.4% advantage betting on don't come. If you strictly bet that way you'll do slightly better than otherwise. That's an exploit, not a hack.
There are a couple different phenomena I'd like to discuss concerning exploits, but for now, I'll just talk about the effect on gameplay. For the first consideration, is this a multiplayer game? Ruining the Morrowind economy is one thing; scamming people in Diablo II is another. Generally speaking, if you're screwing over other players it's not a nice thing to do. If you're just making infinite gold that's less troublesome. But that sort of bug tends to get patched relatively quickly.
For example, early on in WoW you could easily script a fishing bot that would sit around in Stormwind and fish. Leave it running, you get stacks and stacks of fish, which you can sell to vendors. That was how the early gold farmers got their stock. They fixed the problem relatively quickly by making the fish you catch almost worthless. Not an ideal solution, but I don't know how you could better solve it. Err; how better it could have been solved.
If you're playing a single player game, do you use the exploit? The question you have to answer is how does that affect your enjoyment of the game? Take the potion example from above. Sure, you feel clever when you discover the exploit, but being able to make completely overpowered potions (yeah, that's another part of it. If you have a higher intelligence you make better potions. You can make potions of intelligence. With infinite potions you can make insanely powerful potions as well) obviates a lot of the exploring old ruins and discovering treasures that makes the game interesting. On the other hand, in Evil Genius there's a short time at the start of the game where you can steal from the world but the world can't fight back. So if you stop completing the objectives at that point and just loot you can get effectively infinite gold (just leave the game running overnight). But since the acquisition of money mechanic in the game is essentially another timesink I don't mind bypassing it. (I've already complained about the timesinks here.)
To think of it another way, if I'm playing through the Starcraft campaign there's not much point if I use the invulnerability cheat. (Power Overwhelming in the original. Don't know about Starcraft II). On the other hand, if I've already tried this stupid battle three times and I'm losing again and I don't like playing the zerg anyway and I just want to see how this story continues already and... and... yeah, then I don't mind using it to get to the next mission already.