Hi MrBloby,
There's a lot of options available, but not quite a simple as running a progam without installing it first, since Microsoft Office for example need settings installed in the registry and system files installed locally.
CITRIX would be a solution, altough maybe a bit costly for just 10 PC's. You'll need at least a single server, where all the applications are installed and pulished on. All the clients will have CITRIX client installed, and can then access any application published on the CITRIX server from any of those clients.
Novell is another solution, if not an old solution, where each of your PC's boot to the network, and the operating system and applications are loaded over the network, instead of the local HDD.
If your looking for quick and free solution, you could look at Terminal Services client. This gives the user an entire desktop of the PC/Sever your users connect to. Read more here:
Terminal Services 32-bit Client
These are to name but a few popular solutions. If you would like me to expand on any of the above, let me know.