Rather than bring my three favorite games, I'd pick titles with the best replay value. And there'd have to be some variety within the trio.
Tenshi no Uta - One of my favorite RPGs. Played through it three times in one week and was up for another go, but there's so much other stuff to play... which wouldn't be an issue in this hypothetical house.
New Adventure Island - The best time-wasting game ever. Fast and fun. Beat it a few dozen times over the last year or so.
Macross 2036 - Fantastic shooter with a soundtrack that I could listen to forever. Different difficulty settings mean different game plans, boosting the replayability. I tore through it about a million times during the first few weeks after I'd purchased it.