Do they like challenges? Dark Souls, Demon's Souls, Devil May Cry and Dragon's Dogma would be good choices.
If they like lots of action: (see challenging games list), Sly Cooper, Prince of Persia and Lollipop Chainsaw would all be splendid choices.
Fantasy settings? Elder Scrolls series, Kingdoms of Amalur: Reckoning, Dragon Age: Origins, Dragon's Dogma, White Knight Chronicles and anything in the Tales of Series would be awesome choices.
If they're major music lovers then I would recommend Guitar Hero, Band Hero, Rockband and DJ hero as pretty solid choices.
Choose something easier, more casual, first. If it's too easy for them, pick something more challenging. Too hard? Something a little bit easier with a bite would be desirable. I would first ask them what kind of setting they like. Cyberpunk, Steampunk, Fantasy, Sci-Fi, War, Medieval, that kinda stuff.