Will a bitcoin miner work for other currencies? If I purchase a card (or similar device) that claims to mine Bitcoins at 10 GH/s, will that device also work for other currencies?  That is, would the device also work on a multi-pool for litecoins, dogecoins, etc?
ASICs (Application-specific integrated circuits) are especially manufactured for one specific hashing algorithm. Therefore, a Bitcoin ASIC using SHA-256 will not work for Litecoin or Dogecoin as they both use Scrypt. One example for ASICs are the Butterfly bitcoin miners.

There are altcoins that also use SHA-256, such as Freicoin, Peercoin or Namecoin. An overview can be found at altcoins.com.

CPU and GPU can be used for any Coin, but the number of hashes will be different. A card mining SHA-256 (Bitcoin) at 10GH/s will produce much fewer hashes in Scrypt (Litecoin, Dogecoin), because Scrypt is much more complex.