In many cases, yes. Some countries require exceptionally strong encryption but for the most part, a VPN will get you past any governmental interference. Bear in mind that many (but not all) countries require that the VPN log certain information, typically the username, timestamp of login and logout, and total bandwidth consumed. If required to keep the data by law, it will be stated in the Privacy Policy or the Terms of Service. In the event of legal request, the VPN is required to hand over this information, as shown by the Hide My Ass affair, where data surrendered by the VPN was instrumental in the identification and arrest of Lulzsec hacker Cody Kretsinger.
A VPN is for concealing your online daily affairs and normal surfing habits from hackers and spies – it’s not a carte blanche to break the law. Anybody thinking they can use a VPN to commit great hacking deeds is extraordinarily naive.
That all being said, there are VPNs located in jurisdiction-free zones that do not keep records of any kind.