Physical puzzles, like the Gordian knot above. I also like the Rubik's cube, but I don't know how to do the last layer.
Computer games, like Myst, Riven, Uru, Portal, Nancy Drew, all the ones with puzzles. The Myst series is by far my favorite. You should try them!
Puzzles on paper, like Sudoku, logic grid puzzles, and (a new favorite) nonograms. You should try a nonogram out here, but you will have to google an explanation because the site is from Russia. :-)
I watched Stevo solve a Rubik's cube. You could ask him to teach you.
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