Oh my, what a bold question! I’m not sure if I can group them all together, so I won’t :)
Board game: Carcassonne. Everyone can play it, the game changes with the number of people and who those people are, it can be made longer or shorter, you can cooperate or not, and it doesn’t take up a ton of space.
Video game: Rock Band is great, I would group it with DDR as great games I like coming back to and playing with friends. For single player, there’s a special place in my heart for any version of The Sims, extending to Sims and Tycoon games in general. Rollercoaster Tycoon is a classic.
Roleplaying game: D&D is good, but so far my favorite has been Lowlife. It’s a crazy world where humans are long gone thanks to nuclear war, and the only living things are things like sentient pastries, giant earthworms and roaches, piles of goo, etc. Very crazy and fun!