Both my bathroom and kitchen have ugly tile on the walls. Can I paint over them?
Technically, you can paint almost anything if you use the correct preparation method and the most durable paint available (usually, that means one that's oil-based). What's your reason for wanting to cover the tile? Are you simply trying to hide an ugly surface in a rental unit or is this an investment in your home? Your solution needs to match your goal.
Paint away if you want something quick and cheap and don't mind getting a little dirty; you'll need to scratch up the surface of those tiles for the paint to adhere, which will create a lot of dust. This is a temporary fix, however; over time, the paint will chip and become scratched. And remember that painted tile still looks like painted tile.
If removing it is too time-consuming, you can cover it with drywall, giving you a smooth surface. You could also cover the offensive tiles with new ones – choose something timeless. I like greys, black and white and generally avoid beige as it tends to look dull. For a classic, clean look, go with glossy white subway tiles in a running bond pattern. You'll never tire of them. The cost of installing them might not be nearly as bad as the headache you'll endure from painting those tiles.