Is there any free database of hashes of malware? I'd like to get a real database of those hashes, so is there any place where this is possible to collect data?
I've found http://www.team-cymru.org/Services/MHR/, but they don't offer a real database, only API access..
If not, do you have any idea how to collect it on "my own"?
You could ask these guys, as they might know. As a general rule, these databases are the assets of anti-virus companies. They don't really give them away (in readable, re-distributable, un-restricted form), and use them as one base for competitiveness in the market.
Open source anti-virus and scanners for mail servers might point you in the right direction.
You could try and reverse engineer the definitions of popular anti-virus vendors and create a new database with the data extrapolated, but they likely won't be compatible with each other and use different hashing/scanning methods ... it might also be illegal but IANAL.
What about pulling the database out of SpyBot (or whatever anti-spyware system the cool kids are using these days)?