With the news of collisions and reductions in attack complexity in both MD5, a commonly used algorithm for checksums on file downloads and integrity checkers, and SHA-1, a commonly used cryptographic hash algorithm in many encryption products, this brings up the question of where to go next, if you are implementing software which uses cryptographically strong hashing.
The SHA (Secure Hash Algorithm) family of algorithms, validated by NIST, and standard hash algorithms for cryptographic use, contains not only SHA-1 but an older algorithm called SHA-0, for which attacks have also been reported, and the SHA-2 family, which consists of SHA-224, SHA-256, SHA-384 and SHA-512, collectively.
SHA-256 forms a new minimum recommendation, in many cryptographers eyes, given the attacks on SHA-1. Whilst these attacks do not rule out SHA-1 for general use, in order for new software making use of hashing algorithms to be secure for the near future; perhaps a decade, it is important to prepare for the attacks on SHA-0 and SHA-1 becoming more feasible, especially as the cost of computing goes down, and the power continues to rise.
SHA-224, SHA-256, SHA-384 and SHA-512 are all named respective to the number of bits in the output hash. The more output bits, the harder it is to create a collision, in general, unless there is a weakness in the hash function itself, as has been found in SHA-0 and SHA-1.
Of course, the SHA-2 family are based on SHA-1, with slight differences in design and larger output, so it is possible that these have potential attacks also, but the size of the brute-force space is dramatically increased, and so these variants of the SHA family will withstand attack for longer, and should prove reliable for the near future.
Looking into the long term, few solutions exist currently that are not based on the SHA format. There are two main contenders, currently, in the form of the RIPEMD family, and the WHIRLPOOL family.
RIPEMD comes in the following flavours, in each case, the number represents the hash size in bits: RIPEMD-128, RIPEMD-160, RIPEMD-256, and RIPEMD-320. RIPEMD-128 is a replacement for the original RIPEMD, which was found to have security issues, whereas the others all increase the output size, and therefore the associated security. Again, this family is based on a construct which has been proven susceptible to attacks in the past, so it is possible that the entire family could have weaknesses.
The other main alternative, WHIRLPOOL, has no known attacks, and has had two major changes to further improve its security.
WHIRLPOOL is a 512-bit hash function. The changes mentioned involve a change from a randomly generated s-box (substitution box) to one designed to be cryptopgrahically stronger, and also easier to implement in hardware, along with a change in the diffusion matrix.
Some leading cryptographers are calling for new cryptographic hash functions to be designed, perhaps in the same design-by-committee method as the AES encryption standard.