What category of computer or video game is this?

What would you call the category of games that include things like Mario Brothers, where your character moves around through the environment avoiding dangers and collecting prizes? I wanted to look for some downloadable games like that, but don't know what that category is called.

I know it is not like arcade games where you match squares or tetris or pacman, it is not puzzle solving where you go around looking for different tools that you then use to interact with other people/situations, it is not any kind of fighting game.

If I wanted to do a search for new games like Mario, what category would I search for?