I can't get a screenshot because cursors are the only things that DON'T appear in those, but, seemingly at random, this awful long cursor replaces the regular cursor. I tried to draw it in Paint but it's hard for me to know where exactly the cursor is pointing! 
This cursor has other states too: it substitutes a bunch of upward arrows in a vertical line for a hand cursor, a ladder with a bunch of diagonal lines sticking out and pointing down on either side for a resize window cursor, etc.
Eventually, if I right-click/control-click enough, it goes away, but not before my monitors go black for a second, and the computer seems to freak out a little bit (like it's redrawing stuff, but I I may just be making that up).
What is this? Is it actually a built-in feature that's trying to help me in some way? How do I get it to go away permanently? If it's relevant, I'm remoting into the computer this is occurring on.
Best Answer
Sounds like a graphics driver crashing based on the black screen and full redraw - look for a pop-up in the notification area next time it happens. In the meantime, check for updated graphics drivers for your graphics card.