The Secure Hash Algorithm (SHA) is a US standard, developed by the National Institute of Standards and Technology (NIST). SHA-1 is a revised version, published in 1994. It produces a 160-bit hash, which is more secure than MD5's 128-bit hash. It is defined in RFC3174 .
There are several further revisions of SHA, described in the SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions document on the NIST Web site.
It is expected that a revision of SHA will replace MD5 as the most popular hashing algorithm.