is there a way that when a user clicks some link to play a windows game saved on some server to just have the game run from the server without giving the user the option to download it?

That's the reason for using java applets and java programs: you can run the program but not keep it. That's been an idea for a while, but I don't know how to do it. Microsoft, of course, had their idea of charging people to use Office over the internet. I don't know what's going on with that though. Sorry this couldn't be more helpful...

I certainly hope there is no way to run arbitrary native code by simply clicking a link!

There are various IE holes that could be used for the purpose, but once they get patched you need a new distribution mechanism, perhaps another hole. This would, however, cut out all those who use netscape\mozilla\opera\links\amaya\whatever, and bear in mind that a windows binary will cut out mac\linux\solaris\whatever users.

The way that HTML works, though, means that somebody is always going to be able to save your executable to their own computer. It's possible to save most java applets to disk,as well as quicktime movies that aren't carefully munged. (Some quicktime files just tell the player where the actual movie file is located)