If you play a violin without one of its strings, does it ruin the violin? I've heard it does, but didn't feel like trying it... If it does, are there any other problems that can happen because of playing without one of the strings?

Assuming it does ruin a violin: Will it also ruin other stringed instruments, like guitars, if you play missing one of the strings?

The best place to ask is probably the Pegbox section of Maestronet, which is full of luthiers. It's not so much the playing as it is having strings missing because the instrument is under a lot of tension. You have an uneven load. I don't know if it could warp or crack the instrument. There are lots of stories of famous violinists who continued playing on 3 or even 2 strings if one snapped during a performance.

Paganini didn't see a problem with doing so with his strad...He probably even did it on purpose after a while...

Paganini broke strings, and some say it was for showmanship, but I would not think that he would have left his violin partially unstrung. Each of these strings exert a tremendous amount of tension, and if some strings are missing and others are on and tightened that can't be good for the instrument.

It doesn't ruin the violin to play it with a missing string. It hurts to violin to have a missing string and have the other strings tightened.