Probably 'Master & Commander: Far Side of the World', 'cause it's a great movie.
And the other would probably have to be a blue movie of some kind. If dirty films are out of the question, it'd be 'Castaway', not so much for enjoyment, but as a tool for surviving island life.
I would think the last thing you would want would be anything with desert islands in it. If you must though there's always Castaway or Cast Away. I know which one of those two I would preferÿ
I so wanted to contribute when I saw the title, but it is just way too hard. There are too many films from each genre I absolutely love and watch regularly.
Besides, I question anyones ability to watch the same two films over and over and over again without getting just a shade fed up, and wanting to see something else - probably getting a bit too serious and analytical there !!