disclaimer: These are all quite derogatory, so be careful about when and where you say them. -funny farm -nut house -cuckoo's nest

Another one is 'loony bin', but as with the ones mentioned below, it can be offensive and insensitive to use it.

psych ward, почему ты спрашиваешь?

Another informal term sometimes used in the UK is "mental hospital"; - it's not exactly slang, but it certainly would never be used any an official contacts to designate such an establishment.

"Asylum" is an older word that is still sometimes used, though not by those who work in the field. I has some derogatory overtones, but isn't as demeaning as the three that Jonathan Kimball mentioned.