Not for illegal activity, according to an article on Tech Herald:
"Logs, seized equipment, and testimony from those arrested, seems to be the undoing for those connected to Anonymous and LulzSec. ...According to HideMyAss.com, ...services such as ours do not exist to hide people from illegal activity. We will cooperate with law enforcement agencies if it has become evident that your account has been used for illegal activities
The service stores logs for 30-days when it comes to Website proxy services, and they store the connecting IP address, as well as time stamps for those using the VPN offerings."
Furthermore - if you're using a VPN service to stay anonymous, you're only staying anonymous from whatever you're accessing, not the VPN service itself.