1. cmd5.org (paid service)
   MD5, Double MD5, Double Binary MD5, and SHA1
   ">24,000,000,000,000" MD5 (>2 ^ 44.448)
   >24,000,000,000,000 total (>2 ^ 44.448)
   They have 160 TB of disk and 24 trillion (6.67 bytes/password). They are getting closer to 3 bytes/password. Once you start going less than 3 bytes/password it gets kind of slow. They used to have 80 TB of disk and 7.8 trillion (10.26 bytes/password).

2. HashKiller.co.uk (New home for MD5Decrypter.co.uk)
   NTLM, MD5, and SHA1 (* and ** are brute forced which is why it is missing 9,120)
   312,072,522,943 NTLM (2 ^ 38.183)
   829,726,652,095 MD5 (2 ^ 39.594)
   312,072,522,943 SHA1 (2 ^ 38.183)
   1,453,871,725,341 total (2 ^ 40.403)

3. Nitrxgen.net
   MD5
   1,127,962,538,784 total (2 ^ 40.037) [plus some dictionaries with rules, but password count not given]

Honorable mentions:

• c0llision.net (defunct)
  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)

• TMTO.org (had this database in 2007)
  MD5
  308,288,137,503 total (2 ^ 38.165)

• TobTu.com (it's been down for a few years, I'll get it back up "some day")
  MD5
  50,529,455,839 total (2 ^ 35.556)

• inout's (Was just a test and currently down. Also the post about it was on hashkiller.com which is defunct and archive.org is missing it [topic ID was 4958.0])
  MD5
  ~44,450,922,496 total (2 ^ 35.371)

If someone wants to give me a server with 12, 8 TB hard drives in it (or around $5,500) 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.