Currently Online 
Great thread idea!
I know collections are fair game, but I'm going to omit them to make this a little harder for myself...
1) The Legend of Zelda: Breath of the Wild (NS)
I absolutely need a Zelda game in my life, and this is not only the best in my opinion but the one with the most value.
2) Animal Crossing: New Horizons (NS)
Honestly, this is the only game I'd truly need on a desert island. I've already logged 600+ hours, and I could go on indefinitely.
3) Mario Kart 8 Deluxe (NS)
This is the finest racer in my book. Plus it's loaded with replayable content, and supports online multiplayer. Hopefully the island has a hard-wired connection 
4) The Elder Scrolls III: Morrowind (Xbox)
My favorite TES game, and one that I could play for dozens and dozens of hours.
5) Super Mario 64 (N64)
This game is my childhood and I love it dearly 26 years later. I can definitely see myself replaying it again and again.
