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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!
Partitioning a single server to appear as multiple servers has been increasingly common on microcomputers since the launch of VMware ESX Server in 2001. The physical server typically runs a hypervisor which is tasked with creating, releasing, and managing the resources of "guest" operating systems, or virtual machines. These guest operating systems are allocated a share of resources of the physical server, typically in a manner in which the guest is not aware of any other physical resources save for those allocated to it by the hypervisor. As a VPS runs its own copy of its operating system, customers have superuser-level access to that operating system instance, and can install almost any software that runs on the OS; however, due to the number of virtualization clients typically running on a single machine, a VPS generally has limited processor time, RAM, and disk space.