[java] How can I hash a password in Java?

In addition to bcrypt and PBKDF2 mentioned in other answers, I would recommend looking at scrypt

MD5 and SHA-1 are not recommended as they are relatively fast thus using "rent per hour" distributed computing (e.g. EC2) or a modern high end GPU one can "crack" passwords using brute force / dictionary attacks in relatively low costs and reasonable time.

If you must use them, then at least iterate the algorithm a predefined significant amount of times (1000+).