Modern block encryption algorithms are so secure that trying to keep the choice of algorithm secret usually results in more harm than good! An encrypted message is garbage if it cannot be successfully decrypted by the recipient. And if you're going to the trouble of encrypting it, that implies it's a very important message. So it's best to make sure there is enough information in the message so the intended recipient has all the information they need to decrypt it - apart from the secret key, of course.
With modern block encryption algorithms, they are of high enough quality that there aren't known statistical tests to reveal the algorithm used. In the practical sense, however, there is sufficient data to indicate the algorithm used, such as an SSL header, PGP header, an X.509 certificate, etc. If not, there often is something else in the context in which it was found, such as a file named "Secret_Plans.DES", or examining their computer and finding a copy of AES128.EXE.
Classical enciphering algorithms, such as Vigniere, Caesar ciphers, Playfair cribs, etc., will indeed have statistical attributes that can be analyzed, and the algorithm surmised.