There are multiple VPN providers who claim that they don't log your activities. Are they being truthful? What if some users use their networks for illegal activities? When the law enforcing agencies come knocking will the VPN providers go to jail since they didn't log it?
The only way for you to know is if a given VPN provider (or an ISP for that matter) gives you access to their systems for you to see the configuration. And this is very likely to never happen on a large scale manner. Therefore, you have to trust their claims and/or some third party auditing company which has done that work and vouch (with certain liability) for such statement.
All providers based in countries with modern legal systems have to comply with the law requests. If a judge orders them to log data from some user or certain type of activity they will have to do it or face the legal consequences (which vary from country to country...) of not doing so. But they can disagree with the judge's decision and fight, though it will get to a point where either they have to help the legal system or the legal system has to prove further that they need to break the very important right to privacy in such jurisdiction.
In any case, it is likely that the VPN services are not liable for the activities of their users in many jurisdictions.That being said... they may not be liable for the past activities and they can offer no help to any law enforcement since they do not have logs, but should they get a formal request from a judge (and do not fight it in court or do so but lose) they will have to either shut down their service or do what the request says (which is likely to say which user should be monitored).
Some of the fundamental criteria you need to be aware of are not just related to traffic logging itself. The below link offers a fairly comprehensive view of aspects to be considered before buying a VPN service.
- What country is the service based in? Local regulation regarding data disclosure/storage trumps all other considerations more often than not.
- Logging practices. Key points of inquiry include DNS queries performed, timestamps, bandwidth consumed. In essence, making sure minimum possible partial logging is performed, to avoid meta-info (i.e. timing) based privacy concerns.
- Payment method, is it anonymous? Do they require a non-temp email address? Having the potential to commission the service itself anonymously.
- In case sensitive information does get exchanged prior to the service start date, what are their secure exchange practices (i.e. PGP).
The "Privacy Logging" column should help you choose.
The only way to be sure that a VPN provider won't log your activity is to use a VPN that doesn't require any personal information to register and login or that can't match your registered account with your login.
For example a VPN that would use an anonymous token to login. I don't want to recommend a vendor in particular, but I think there is only one that actually use anonymous tokens.