Which TrueCrypt Algorithm is the safest?

Using TrueCrypt 7.0a, the most secure method of encryption is: Use the AES-Twofish-Serpent cascading encryption with the XTS method. Use the Whirlpool hash algorithm. (SHA-512 is a very close 2nd place here... it's debatable... I'm leaning towards Whirlpool because SHA-512 is already having a successor developed because of fears that it is based on an older SHA-1 that has been compromised.) MOST IMPORTANT is to use a VERY strong password. 20 to 30+ characters, uppercase, lowercase, numbers, symbols. Use Microsoft's online password checker for a strength test. You can also use Keyfiles to further secure your password.

I recommend the AES-Twofish-Serpent over the Serpent-Twofish-AES because you want the outermost encryption (AES will be the first layer they need to break) to be the most standard in the industry. That one is the most tried and true and the most tested of all of them. Plus, if someone assumes a file is encrypted with AES, there's no way of seeing that is is then encrypted with Twofish... so they do all this work to break the AES, only to find that Twofish stands in their way now. And then again after Twofish they run into Serpent, which is the biggest beast of them all (even though it is less used / tested than AES, it still has a much higher security margin than AES)

If you do use Keyfiles, I'd recommend having TrueCrypt create 3 keyfiles for you. Create one keyfile for each hash algorithm they provide. You might also add some .jpg's and some .mp3 files as well. I would make sure to make each keyfile read-only however.

This is probably overkill though.

these are the results of the voting in the final round of the AES-contest:

Rijndael 86-10 = 76
Serpent 59-7   = 52
Twofish 31-21 = 10
RC6 23-37 = -14
MARS 13-83 = -70 

(http://csrc.nist.gov/archive/aes/round2/comments/20000523-msmid-2.pdf, linked via truecrypt serpent, read that one as well).

so, for a variety of reason Rijndael became AES, which is the successor of DES (and 3DES).

and, just because it popped up today on news.ycombinator.com, the story of AES:

http://www.moserware.com/2009/09/stick-figure-guide-to-advanced.html

The cascaded ciphers (AES-Twofish-Serpent, etc.) should be the most secure. Your data is encrypted with one algorithm, then the output from that is encrypted with the second algorithm, whose output is encrypted with the third algorithm. According to the TrueCrypt documentation, each algorithm uses a different key, each derived from your passphrase.

If a vulnerability is found in one (or two) of these ciphers, your data should still be secure, as an attacker would still not be able to break the remaining ciphers.