First of all VPNs provide a anonymity in the internet. however not even a single VPN provider can assure that we will be safe no matter what. some people will say buy a premium one so that we are secured. but i would say thats not the case.
Let me point out an example. In 2011, Hidemyass a pretty good pro VPN provider bailed out on one of his user as the pressure from governments and corporate giants grown bigger. One hacker used hidemyass to cover his hacking tracks when he pulled out one of the biggest hacks in SONY's server. Eventually Hidemyass gave out his original IP and Name when they got a official call. Here's the link for that news: https://www.theregister.co.uk/2011/09/26/hidemyass_lulzsec_controversy/
So my point is that even though if you are using any free or premium VPN you are the one who should be more careful at what you do. If you want to become truly anonymous in the web, you have to use a combination of TOR and Free or premium VPN.
You can again increase the chance of anonymity by using this TOR and VPN in a virtual machine.
Again we can increase it by using TAILS (solely created for maintaining anonymity) with TOR and VPN.
You need a VPN in these 3 cases, it can be premium or free.
So i am gonna list out the some of the free VPNs out there whose privacy policy are fairly good.
You can find a detailed review of all these providers in my website: Best Free VPN 2018 - IGoTechnical