Are there free online penetration testing labs that I can safely hack with my computer?
I have seen the offensive security penetration testing labs; they are amazing but costly. Is there any other online virtual penetration testing lab I can SAFELY conduct penetration testing and exploitation against? I do not mean machines I can download, I mean online labs or sites.
As you say online labs, are you talking web apps / web servers rather than OS, or are you looking for online virtualised windows/linux labs? if you are looking for web, then first take a look at hack yourself first (from Troy Hunt) and Hack This Site (that's a name, not an instruction ;- ) )
Here are my favorites for practice:
GhostSec's pentest labs - Only VMs all hosted online.
VulnHub VMs (only downloadable VMs)
root-me.org is pretty awesome - it's got both web challenges as well as hosted VMs that you can deploy and attack.
hackthissite - name says it all, we app pentesting.
CTF365 - As you've probably figured, they have year long CTFs. It's been some time since I last used them, so I'm not sure if they've started charging for even usage.
Hack The Box - A competitive platform.