Simple password encryption
As mk says, SHA1 or MD5 are the standard ones, along with SHA2.
Update: As processors have gotten faster over the years, hashes have gotten more brute-forceable. It's now recommended you use bcrypt.
What you want is more generally called a cryptographic hash function. Cryptographic hashes are designed to be one-way (given the resulting hash, you shouldn't be able to derive the original input). Also, the likelihood of two arbitrary strings having the same hash (known as a hash collision) should be low (ideally 1/number of hash values).
Unfortunately, just because your passwords are hashed doesn't free you from having to try really hard to keep the hashed versions safe. Far too many people will use weak passwords that would be vulnerable to an off-line brute-force attack.
Edit - several people have also already pointed out the importance of using a salt. A salt is a constant value that you mix in with the input before using the hash function. Having a unique salt prevents off-line attackers from using pre-computed tables of common passwords (rainbow tables) to brute-force your passwords even faster.
MD5 or SHA1 + salt.