koding.com has a free VM running Ubuntu. The specs are pretty good, 1 gig memory for example. They have a terminal online you can access through their website, or use SSH. The VM will go to sleep approximately 20 minutes after you log out. The reason is to discourage users from running live production code on the VM. The VM resides behind a proxy. Running web servers that only speak HTTP (port 80) should work just fine, but I think you’ll get into a lot of trouble whenever you want to work directly with other ports. Many mind-like alternatives offer similar setups. Good luck!
I had the same idea as you but given all restrictions everybody keep imposing everywhere I feel that I must go out and pay for a VPS.