For a new player:
1) Minecraft (On the top of my head, would get people hooked)
2) Machinarium (Or any other puzzle game - get them thinking ^^)
3) N: The Way of the Ninja (Not as easy as those above, but I can't see one not liking this game)
4) NHL 98 (If there are newer ones, I wouldn't know, but that one rocks!)
5) Half Life (It ain't that hard, and I need a FPS title here)
My opinion would be give a couple of great games of different genres, they'll like something.
As for "must play":
1) Gothic NotR (I'd place Gothic 1 here as well, but it's more of the same)
2) The Elder Scrolls: Morrowind (Maybe the other TES games are good too, but didn't play them.) Now, Morrowind is great and all, but the thing that made the biggest impresion was the thunder. 'Nuff said.
3) Mech Warrior 4. If Gothic NotR wasn't my favorite game of all time, this would be.
4) Half Life. 'cause you're not allowed to play FPS games if you haven't played HL.
5) Starcraft. The game may be old, but I'll be damned if it's not one of the best RTS' out there.
I could place more here, like SWKOTOR, Mirror's Edge, NWN, M&B, SMB, The Witcher, Heroes of M&M III (or V), and so on, but that wouldn't be 5. To many good games out there to count D:
Now, I haven't played some games that I heard were good, so my list might've been different had I played them (Would probablly include Portal). Be it as it may, these are a must.
Also, a special place for Minesweeper ^^
EDIT: I CAN'T BELIVE I FORGOT VAMPIRE THE MASQUERADE BLOODLINES D: