Card can be used for two things in general: as a rule-reference to the game and as generator of a random effect. In most cases, the use of cards combines these two.
In general one could say that card effect (drawing a card with a certain game-effect) is just a replacement of text in the rule book. As drawing cards generate a random effect, instead of throwing a few dice and looking up the result in a reference guide, you now get the event spelled out directly. Especially for games that include many different random effect, using cards is very good option.
A lot of games use (randomly drawn) cards for mission determination. The card tell the player under what circumstances he/she will win. A typical example is Risk. Other games that use cards in this way is Pictionary.
In some games players are handed out cards concerning the role they are going to play, with all its advantages and disadvantages. Typical examples are Lord of the Rings (by knizia) and many fantasy games.
Event cards / Reward cards
A large amount of games use card effects for special events or reward. Under circumstances a player is forced or has the option to draw card. In general these effects overrule the standard game rules. In addition, most games contain more than one kind of cards, you may have lucky cards, circumstance cards, etc. Also you may have cards that last for a short period and card effects that may last during the entire game. In addition an event might give you a special item (that you have found). Next to money this might be something of use. Typical examples are given below (Warhammer Quest)
Treasure chest cards may represent something you have found. The Dungeon card is used for tile laying, it gives you an idea of the room you have entered and what might be discoverd (randomly). The event card tells you what you have encounterd (e.g. when you entered a room). Interesting facet in this case is that the backside of the cards only inform you about the nature of the card, but not of the content. This in contradiction to the following cards:
In this case (Dragon Quest) the back side tells you what you have found, while the play side tells you what happens.
This is another example of a 'treasure card', the back side tells you that it will be a tool, the play side what it exactly is (and how you can use it). Btw, cards do not neccesarilly need to have the format of a regular card:
DungeonQuest has loads of cards, where as the layout of the card corresponds with the event on the board (the open-a-door-card has the format of a door, etc.). Note, this make the game component look rather shabby (many differents sizes of cards and, especially in this case (Dungeon Quest), of poor quality).
The most popular game using cards for random event is propably monoply where you have draw your chance cards. As many other games, moving around is accompanioned with card drawing to see what happens in certain situation. A typical game that uses Card-event heavily is Dungeon Quest (Games Workshop). Although at first site there are far too many staples of cards, once you get the hang of it, it's quite intuitive, as all effects are explained on the cards. Thes types of games are typical a combination of racing and tile laying (btw. the older Games Workshop games are known for their many cards (the newer ones (eg. warhammer) are known for their fat rule books)
A lot alike the cards mentioned above are cards that can be used / played by the player to influence the game. The most typical example is Roborally, where you program your robots by cards.
These cards are drawn random and are to be put in a sequence that suits the player.
Another game that uses cards for this purpose is James Bond (Jumbo).
Changing the odds
Another mechanic to think about is what to do with used cards, should they be removed from the game, put on the bottom of the pile, put back to a players hand, shuffled back into the stack, etc. Note that there is a major difference between putting cards back and removing them from the staple (e.g. putting them out of the game or have players hold them). Also make a difference between putting used cards on the bottom of the pile and shuffling the pile every once in while. Counting / collecting (certain) cards may make a game 'broken'.
Tile laying games also use cards/tiles for setting up the board. I guest Dungeon (although not a very great game, but pretty funny) is typical example of using cards for both tile laying and generating random effects (this game has LOADS of cards).