Indiana Jones and the Infernal Machine was the first game we played on a 'modern' PC and it blew us away.
This is mostly coming off of the Amiga, so it went from things like Prince of Persia, Corridor 7, Dragon's Lair, etc. to that. Our other PC could run things like Close Combat, wargames, really old stuff like Alone in the Dark maybe, etc. So Infernal Machine's brought graphics and awesome water effects etc. were really cool to see on a home computer. Other games from that era were pretty wowing, like Shogun Total War's putting a buncha dudes on screen, for example. We had a 9-gig harddrive and I remember Shogun being the first game to really press me for space. Adjacent to it was the Braveheart game, though it was totally wrecked by bugs. Morrowind was probably the last from that timeline. It was my first experience in an open-world 3D RPG so the idea of just walking wherever you wanted to and it was all in first-person with a little dude who physically equipped armor and stuff kinda blew my mind.
Half-Life 2 had some innovations like physics and the speech/mouths that felt like a leap ahead. Purely on visuals alone, Ninja Gaiden and Splinter Cell Chaos Theory really wowed me at release. Chaos Theory especially looked like the fukkin' truth of graphics, totally future fantastic, future so bright, etc. but instead consoles ended up stalling out and I don't feel like they ever really got that far beyond it. There were a few tech demos from this era that were also quite enthralling, like the TF2 stuff before it went into cartoon mode, Duke Nukem Forever's tech demos, even things like the Call of Cthulhu Dark Corners of the Earth tech demos, which ended up looking nothing like the game but the DNA for all these things was there. Company of Heroes I think was the last game to wow me in a technical sense. At release, it looked absurdly good for an RTS game. I even remember the PC Gamer shots of it trying to explain that yes, they were in-game, and yes it wasn't an FPS. Lot of other pretty games from that era, but nothing else that really got my attention in a technical sense.
edit: Oh and Silent Storm, which was another Chaos Theory-type moment where I thought it was the future, but instead it just died on its own, an insanely advanced computational engine that got fed into two sequels, a game called Tin or something, and a Russian movie spinoff of vampires or whatever. Such a disappointment, much like the middle 5 pages of this thread.