If you have to write a hash function for something important (i.e. a .NET GetHashCode method or a C++ hash traits class), don't design your own. Steal one that has been well-tested. One of my favorites for speed, simplicity, and quality is the "Jenkins One-At-A-Time hash" (aka joaat hash - "one-at-a-time" refers to one byte hashed per iteration, though the algorithm is probably still mostly ok if you use a 16-bit char per iteration instead). You can find a good description of it and many others at http://www.burtleburtle.net/bob/hash/doobs.html. For more information, see the Wikipedia entry on hash tables.
If you see any locally-developed hash table implementation that requires a prime number of buckets, you might want to track down the author and suggest a better hash function that doesn't place a prime number constraint on the number of buckets. Prime numbers are not necessary if a high-quality hash function is used. (Keep in mind that the hash table author might be aware of better ways but is remaining backwards-compatible with previous releases or is protecting the clients of the hash table from their own bad hash functions.)
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