This is completely my own opinion, some people might not LIKE these games.
1. Portal: chances are everyone HAS tried this game but its still great, the sequel is awesome too but it's just such a simple and elegant title, a good example of how videogames can make the player think.
2. Zelda: Everyone should play and win one Zelda game, personally I'd reccomend Ocarina of time but so many of them are great anyway. Zelda games are the definitive Adventure game, exploration, combat and puzzles are all finely balanced into an experience that can't be defined in simple words. Suffice to say the feeling one gets when finishing a Zelda game is good, it almost feels like finishing a good book.
3. Sonic the Hedgehog: I'd reccomend all 4 of the main Genesis/Mega Drive games in this slot but to keep it simple, the original game. Technology may have come very far and we may have fantastic new games but no child should have gone without Sonic. A basic game that relies on pure platforming to be interesting and it works, there's a fair level of challenge and is a superb way to introduce young children into videogames. (If you want this option can be replaced with Super Mario World but you get my idea)
4. Shadow of the Colossus: A very typical answer in threads like these but it's justified, the first game I played and found to be, for lack of a better word, beautiful, as a game it works on some of the most basic videogame psychology, you NEED to know what the next enemy is like. But on a deeper level it's such a gratifying experience with some of the most innovative/interesting combat in years.
5. Metal Gear Solid: The PS1 classic that blew open a whole new world of videogames to me, the first time I was compelled by a story in a videogame and took great interest in its plot. The gameplay was rather revolutionary at its time and the boss fights made for great pacing in the gameplay structure. However I would say out of the games on my list this is also the least universal, you have to be a fan of action and how MGS both follows and breaks its conventions, it was also the first game that really made me suffer the consequences of my actions, I originally got the bad ending which left me with a terrible feeling of what was almost guilt.