In refrence to the card game Spades, shmOOnkie has an excellent writeup, but I have a few things to add. There are two other legal bids. Both are worth 200 points, and a team must be losing by at least that much to make the bids. They are also "all or nothing" bids, that is if the team making the bid is unsuccessful, they lose 200 points. The first bid is called "10 for 2." The team must take a total of 10 tricks, and there is no bonus for extra tricks (but sandbags still count). The second is "blind-nil." This bet must be made before the hand is dealt (hence the "blind"), but is otherwise the same as nil.
When one team member goes nil (or blind-nil) the other player can still make a normal bid. The scores of the two players are determined separately and then totaled. So if one player bets nil and makes it and the other player bets five but fails to make it, the total score would be 100 + 5 x (-10) = 50. Also if the person going nil does not make it, any tricks they make is used for their partner's score. For example, if the bets are nil / 5 again but the tricks taken are 2 / 4, the score would be -100 + (5 x 10 + 1) = -49.
There are also a number of different trading rules for when someone goes nil or blind nil. The trades are made before play starts and the players cannot discuss the trade (which suits they need, which they don't need, etc.) so that neither player knows what the other is trading until after the trade. The different trade rules vary by the number of cards traded, the more that can be traded, the easier it is to go nil. The number can also vary between nil and blind nil. The variations I know of are:
nil | blind
-----+-------
0 | 1 (hardest)
1 | 1
1 | 3
3 | 3
3 | 4 (easist)
There is also a two - player variation of the game. The bids are the same (although a nil is much harder to pull off), and there is still just 13 tricks in one hand. The difference is in an interesting deal. One player will shuffle, and then set the deck between the players, forming the stock. The other player will then take the top card and decide if they want to keep it. If it is a card they want to keep, then they put it in their hand and discard (face down, after seeing what card it is) the next card on the stock. If they don't want to keep the card, then it is discarded and the next card in the stock is put in there hand. The first player follows in a similar manner until the whole stock is gone. With this deal each player knows of 26 cards (their hand and discards) that the other player doesn't have, but they can't be sure of which of the other half of the deck their opponent has, thus leaving an element of skill in the game.