In album form (hardly a revolutionary change). The catch is that, on this theoretical island, you only have a CD player (or some kind of portable record player for the audiophiles) and its a bit beat up so it won't play burned CDs (basically choose from your physical Cd/record collection).

So mine are:
1) A Winged Victory for the Sullen -S/T. So its one of my most recent additions, but I would need something in the drone category, and this has overtaken Stars of the Lid, Loscil, M83 and Hammock as my de facto choice
2) Cut Copy - In Ghost Colours. Probably the favourite feel good record I own. Just
3) Iron & Wine - The Shepherds Dog. Its the variety that draws me, like a little jam band got together and decided to play country, blues, rock, reggae, pop...
4) Muse - Showbiz. I would think, all alone, an over the top and slightly embarrassing record would be just as good use as something subtle. Plus there's all the nostalgia bonus points.
5) Arcade Fire - Funeral. Gets picked because its really really good, still.