AES is the U.S. Standard and is the safe choice.  The runners up for the standard were Twofish and Serpent and both are considered to be very strong.  Twofish is the successor to Blowfish and is probably a better choice than that algorithm. 

RC6 was evaluated as a candidate for the U.S. standard but was not selected as a finalist.  I don't know if that was due to flaws in the systems or because of other concerns such as performance, code size, etc.

Triple-DES is still a good choice, but it's slow.  Triple DES uses 168-bit keys, but carries only 112-bit security (because you can do a time-memory tradeoff when triple encryption is used.) DES was the old U.S. standard.  Regular DES uses only 56-bit keys and is not recommended for new products.

Key size is important, but algorithm strength is equally important.  Try to find a copy of Applied Cryptography by Bruce Schneier.  The book is out of date so it won't talk about AES or Twofish, but it will give you a little insight into the types of concerns that go into selecting a cipher.  At a minimum, read the chapters on DES, block ciphers (there are two) and the chapter on key size.  As an alternative, you can find the Handbook of Applied Cryptography online for free in pdf form.  It's by Alfred Menezes et al.

Wikipedia is probably a good place to get some background on the algorithms.

If you want to find papers on the cryptanalysis of these algorithms, look at the proceedings to IACR's Crypto and Eurocrypt conference as well as the Fast Software Encryption Conference.  Unless you have a heavy math background, and until you've read up on block ciphers, you'll probably just want to skim the papers for the results and conclusion.

I hope this helps.