Keccak wins the SHA-3 competition
csrc.nist.gov
csrc.nist.gov
If you're writing a new application, by all means use the new standard. If you have an existing application or have to interface with existing frameworks, use SHA-2.
SHA-2 also has length-extension, which isn't a hash flaw per se, but is something you have to know about if you're building cryptosystems with the hash (as opposed to using something off-the-rack like HMAC).
If you are using HMAC, you really don't need to worry much about which hash you're using. There is to my knowledge no practical attack against HMAC-MD5.
For cryptographic hashing it may make a difference, depending on the context.
Murmurhash and Cityhash are two excellent and fast non-crypto hashes. The FNV hash is also quite good, very fast, maybe not as good as Murmer and City, but has the advantage that if you like running your own, it's super-easy to implement (like two lines of C code easy).
FNV hash http://www.isthe.com/chongo/tech/comp/fnv/index.html
Murmur hash http://en.wikipedia.org/wiki/MurmurHash
City hash http://en.wikipedia.org/wiki/CityHash
In case you're interested, here's two great explanations of what to look for in general purpose hashes (avalanche behaviour and uniformity): http://bretm.home.comcast.net/~bretm/hash/ and http://www.partow.net/programming/hashfunctions/index.html
However, I know several advanced algorithms in the realm of cryptography can be computationally expensive, and as demand for security grows, several of these semiconductor companies have implemented things in the hardware to optimize certain forms of encryption. (I can't remember if it was Intel or AMD that released a chip with some sort of built-in support for security).
This is just a theory, but if they're going down this road, it would make sense for them to develop a highly secure algorithm that they know can be easily implemented and optimized on the hardware level. If they're developing specialized algorithms AND hardware, they can probably take it into account during the design process and further optimize their boards.
Or, a bunch of semiconductor guys are also crypto-geeks. Which is pretty likely anyway :D.
http://ehash.iaik.tugraz.at/wiki/SHA-3_Hardware_Implementati...
Keccak is one of the most amenable to hardware acceleration, but all of the finalists were good in both hardware and software.
Guido Bertoni: http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/b/...
Joan Daemen: http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/d/...
Gilles Van Assche: http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/a/...
Joan Daemen has a PhD, his thesis was "Cipher and Hash Function Design. Strategies based on linear and differential cryptanalysis"
Gilles Van Assche was a PhD student at the University of Brussels studying "classical and quantum information theory" (http://gva.noekeon.org/)
Yes, see here for Keccak implementations http://keccak.noekeon.org/files.html
The C code appears to be public domain. Which might be a problem in regions in which public domain is not a thing but should otherwise be fine for use in most projects.