You did mention computer-only in your original post OP, which would technically reduce the number of games we would be able to suggest as "must haves". Did you really mean PC exclusives? Because many such classics can be found on consoles (whether they were ported to or from the PC is irrelevant here). I could suggest Half-Life (the original) but it was released on the PS2 (with the Decay campaign), or I could mention Command & Conquer but it was released on the PS1. I could also praise Portal 2 but it's on the XBOX 360 too.
But just in case you did mean PC exclusives I'll go with a few, in no particular order (and I know I'll miss a good bunch)...
- Sins of a Solar Empire (I think Trinity is on Steam too)
- MechCommander (played it a lot back in early 2000 to around 2001)
- Grim Fandango
- Galactic Civilizations II (original one is good too, but sequel is better)
- Baldur's Gate 1 & 2
- Dungeon Keeper 1 & 2
- Thief 1 & 2
- System Shock 2 (never played the original myself, can't say if good or not)
- Supreme Commander + Expansion (Forged Alliance, great game in my opinion)
- Battlefield 1942 / Battlefield 2
- Star Wars: TIE Fighter (did not age well in my opinion, but still consider it a must)
- The Longest Journey
- FreeSpace 2 (the original FreeSpace is good, but shadowed by the sequel)
- STALKER (pretty much the whole trilogy, but the original and Call of Pripyat are great)
- Fallout 1 & 2 (especially the sequel, still have it installed right now)
- Homeworld 1 & 2 (have great memories of the original specifically, sequel also good)
- Age of Empires II + Expansion (Age of Kings, classic stuff right there)
- Rise of Nations (absolute must-have RTS that still surpass many within the genre to this day, that is ten years later by now)
- Planescape: Torment (amongst the best RPGs)
- Company of Heroes
- Warhammer 40,000: Dawn of War (referring to the original specifically)
- Diablo 1 & 2
- Rome: Total War (in my opinion still the best overall of the whole Total War franchise, although Medieval II isn't bad at all, I don't consider that one "must have")
- Total Annihilation
- WarCraft III (gimme a slap if you want but yes I think WC3 is a "must have", I really liked the campaign mostly, along with its expansion's)
...and yeah I know I'm forgetting a good number right now.
Also many found on GoG.com would be considered must-haves, most of which are PC exclusives with only a few exceptions here and there (such as Witcher 2 which is also on the XBOX 360).
This is a good list.
But yea most of the games I consider "must haves" are already mentioned.