There’s no way to narrow it down to just 3 games. i have favorite SERIES that have more than 3 games to them:
Black Mesa, Half Life 2, Episode 1, Episode 2 - Let’s face it, Black Mesa will be awesome. When it comes out, I’m almost certain that in my mind it will be considered the first game in the Half Life 2 series. I really shouldn’t even need to go into any detail about this one.
Portal, Portal: Prelude - The same way I’m sure I’ll be considering black Mesa to be part of HL2 series, I already basically consider Portal: Prelude to be part of Portal. However Portal: Prelude should definitely be done AFTER Portal even though it’s a prequel. It’s not only harder, but a lot of the fun of playing it comes from the references it makes to Portal, whereas the fun of Portal is the mystery that playing Portal: Prelude first would actually ruin.
Dance Dance Revolution/In The Groove/Stepmania - I have a steel dance pad for these things. Still worth the money I’ve put into it. There are some 12-25 different games though, not counting the fanmade stuff.
Psychonauts - Best Standalone Game Ever. I have never felt so intellectually engaged while playing a game, and not just from the puzzles, but from the entire setting, plot and mood of the game.
Baldur’s Gate & Tales of the Sword Coast (TUTU - BG on BG2 game engine), Baldur’s Gate 2; Shadows of Amn & Throne of Bhaal - This was my first real introduction to an ACTUAL PC game. The graphics are horribly outdated by pretty much any standard, but the excellent world, storytelling, and characters, as well as the incredible improvements that have come from fan community support make it fun even for playing through today
Shadows of the Colossus (Ico might get included in here, but I’ve never gotten a chance to play it) - Simple, elegant… I’d almost use the term “pure.” Nothing distracts from or waters down the essence of what the game is about. Possibly one of the best examples of art within a game I’ve experienced. Nothing of the characters, the world, or the history of the story of the game are given to you, yet the small minute details reveal nearly everything there is to know.
Metroid Prime (Wii) 1, 2, 3 - I’ve only played the 3rd one of the series on the Wii, I’ve long since been jaded by controls that require the joystick to aim, so I’ll be waiting for the “Play on Wii” titles to include 1 & 2 of the Metroid Prime series before picking them up.
Tomb Raider Anniversary & Legend - These are the first games that I’ve ever played from the series, and honestly the only ones that I have been interested in. Tomb Raider has always sold itself at least partially on the eyecandy aspect, but it wasn’t until these that I felt convinced it was a point worth selling. The controls also came together incredibly well, working nearly flawlessly on a 5-button mouse + PS2 controller combo.
Thief 1, 2, 3 - I’ve only played the 3rd game from the series, and found it incredibly engaging. I still will never forget “The cradle” and it still stands as one of the most terrifying levels I’ve every played. However everyone claims that the 3rd one wasn’t even the best of the series, so I’ll be playing through the earlier games as soon as I get my PS2 controller set up properly for playing them. Unfortunately that means I’m going to have to do all the button mappings manually.
Legacy of Kain series - I’ve only played the first 3 games from the series, and have only beaten the latter 2 of those that I’ve played so far. I have quite a few personal issues with the combat system, but the convoluted storyline, unapologetic antihero main characters and downright awesome techniques make for an incredible fun series so far. the original Blood Omen plays completely differently though, which is why I haven’t bothered to beat it yet.
Zelda Series- I can’t think of a single BAD game out of this set. Only Phantom Hourglass disappointed me to any extent, and Adventure of Link was ridiculously difficult. Legend of Zelda, Link to the Past, Link’s Awakening(DX), Oracle of Ages/Seasons, Minish Cap, Ocarina of Time, Majora’s Mask, Wind Waker, and Twilight Princess all are incredible games in their own right. My favorites probably are Majora’s Mask, Minish Cap, and Twilight Princess.
Half Life - it may seem odd, but i consider this a completely different beast from HL2. There are just too many ways in which HL2 improves over HL1, yet HL1 still holds it’s own against games on the market today. Even once Black Mesa comes out, I’ll still probably play this from time to time, even if I actually keep it installed more for the mods.