They have logs, they just don't keep them very long. (Allegedly.) So in theory, while they might not have logs for a past incident if it's been long enough, they most certainly have logs in very short term and/or can tell who's connected to what at the present time. So while many copyright actors will be too slow to get a hold of said logs, a government actor with significant interest will.
The biggest issue for me is that VPN providers have given me no particular reason to trust them. If I already have reasons to distrust large international corporations that say they care about my privacy, why would I go trust one I've never heard of on the Internet that says it cares about my privacy?
Under EU privacy regulations you could probably demand that your VPN provider gives you a copy of all information they have on you, including logs.
In the EU I've seen this successfully done with ISPs, ie. customers request logs and get a CD by mail. You'll have to insist and it might involve a small service fee.
Probably what is required under Danish "law", which would be every 20th TCP session or so...
Note: I write "law" because afaik the current logging directives have been found in violation of the European Human Rights declaration, I hear a legal battle is pending:
Whether or not your VPN provider gives you any particular reason to trust them - for some of us, the government has passed laws to require our ISPs to be "untrustworthy".
The biggest issue for me is that VPN providers have given me no particular reason to trust them. If I already have reasons to distrust large international corporations that say they care about my privacy, why would I go trust one I've never heard of on the Internet that says it cares about my privacy?