Mainly capacitive screens, that are found on basically 100% of the smartphones and tablets today. There are resistive multi-touch screen too, but they aren't used by pricing reasons and the general need to apply pressure to make the touch work (more adequate for stylus).
There are multi-touch touchcreens with infrared laser grids too. These technology is used to build giant touchscreens. You buy a glass frame that has an invisible grid of infrared lasers and just put it over a big TV to create a gigantic touchscreen. I once used a 40' TV to play Angry Birds and Plants vs Zombies, it's pretty cool.
It's necessary to remind you that these screens highly vary in the amount of touches supported. A multi-touch screen is one that can detect at least two points. Tablets and notebooks almost always come with a 10 point touchscreen, while phones may have less (since you won't use 10 fingers on it).








