I think VLC specifically addressed this issue, but I'm sure it still happens with other video players. Mouse Jiggler is a tiny, handy utility whose sole purpose in life is to jiggle the mouse cursor for you, so that the screensaver doesn't kick in.
It has a neat feature called "Zen jiggle" (I love the name) which jiggles the mouse "invisibily" – meaning, your computer thinks the mouse is moving, while the cursor doesn't actually move anywhere.
The GUI is sparse, and I like that. Just two check boxes. You can't even minimize it or hide it, and I think that's great: this way you can't forget it on, and then wonder why your mouse is randomly jiggling while you're working. Very nice!