I'm pretty sure Doom will be the most popular (and my pick too), but I'll throw a shout-out to Epic Pinball; that Android table was the best one in the game anyway.
Pretty sure I even bought the full game and never ended up getting very far. I also remember spending a little chunk of time on Hugo 3: Jungle of Doom, but could never figure it out enough to progress very far.
Edit: Another one I was trying to recall, the name was H.U.R.L.
Jumping around with the pogo stick in Keen 6 was so much fun. I recently found the full game. Was surprised how hard that factory level was. But the music was still how I remembered it.
A couple of people have mentioned Raptor: Call of the shadows, which was an absolute favorite of mine. Skyforce Reloaded is pretty close in terms of gameplay. I wish there were more games out there like Raptor
I was a huge fan of Solar Winds: The Escape. Cool plot, aliens, dogfights, ship systems management, evil shadow governments, rebels.... what's not to love? It was my introduction to the genre and will always hold a special place
Colobot - don't think it was "shareware" but it absolutely came as a demo on ceebot.com (still hosted there today I believe). Literally THE game that got me into computer programming and whatnot.
Otherwise for actual shareware, I loved Jazz Jackrabbit 2, Crazy Gravity and The Worm (found it!)
I really wanted to play a couple shareware games called Jetpack Joyride, and Hot Chix n Gear Stix as a kid, but neither of them would play on my Windows XP netbook as they had a hard check for if you were on either Windows 95 or 98, even with compatibility mode.
I spent so many hours as a kid on my dad's Thinkpad playing Gravity Well. It came on one of those "50 Great Games" CDs or something like that. The goal is to claim all the planets in the system, which you do by simply landing on them, then building defenses against your opponents. It's so much fun because your ship has pretty realistic inertia and the planets have actual gravity wells. The AI opponents can be quite difficult and aggressive. Challenging and fun, with great sound effects for the time!
This screenshot is from an Internet Archive page for the game, but I'm pretty sure it's only the shareware version. I gotta check again when I get off work!
Edit: I'm 99% certain it's from this exact CD for anyone interested. I've never been able to find a full version unfortunately...
I played a lot of TetriNET and Subspace Continuum with my old online community. Great times.
More detail edit:
TetriNET walked so Tetris 99 could run. Version 1 does not install on Windows anymore (but has a Linux version). Version 2 works, complete with its archaic user registration that asks for too many details.
Continuum is a large PvP arena Asteroids-like 2D space shooter. It's on Steam now. Starts tough to control and with a high skill ceiling, so be wary of the veterans. The Death Star Battle map is a blast with a big group. It feels like trying to speed through a narrow maze on bumper boats during a huge battle.
I played a lot of 2 games that nobody I've spoken to has ever heard of:
Mordor the depths of dejenol
Exile escape from the pit
Both were great, I think exile had been remade by the programmer with a different title too
I was always struck by the similarity to the blue robot on that table to Cyborg from Rise of the Robots and I wonder if there was some cross-pollination there.