1. cmd5.org (paid service)
    MD5, Double MD5, Double Binary MD5, and SHA1
    "7,800,000,000,000" MD5 (2 ^ 42.827)
    7,800,000,000,000 total (2 ^ 42.827)
    They have 80 TB of disk and only 7.8 trillion. They can totally get 25 trillion.

  2. c0llision.net
    LM, NTLM, and MD5
    10,578,558,976 LM (2 ^ 33.300)
    295,413,219,328 NTLM (2 ^ 38.104)
    295,413,219,328 MD5 (2 ^ 38.104)
    601,404,997,632 total (2 ^ 39.130)

  3. MD5Decrypter.co.uk
    NTLM, MD5 and SHA1 (plus some MD5x2, MD5x3, MySQL, LM, and others but these only account for a few million passwords)
    21,188,313,704 NTLM (2 ^ 34.303)
    21,188,313,704 MD5 (2 ^ 34.303)
    21,188,313,704 SHA1 (2 ^ 34.303)
    63,564,941,112 total (2 ^ 35.888)

  4. TobTu.com
    MD5
    50,529,455,839 total (2 ^ 35.556)

  5. TMTO.org
    MD5
    36,436,233,567 total (2 ^ 35.085)

Honorable mentions:

If someone wants to give me a 2U server with 12, 3 TB hard drives in it ($5,000) I could totally be number one.

All the sites I've found are either smaller or don't say how many passwords are in their database.