Well, I had to think about this a lot.
Rise of Nations
My favorite RTS of all time, I think possibly the best RTS of all time. Looking back, it's kind of a mix between the Total War games with their tactical map and Age of Empires with the battles and building. It's much better than Age of Empires, though, and moves faster and has more varied units. It's mostly on here because of how much I played it with my brother one summer, in co-op and just murdering swarms of enemies with rocket artillery.
Counter Strike 1.6
I was really late to the party on this, never played it at LAN parties, never played in a clan or even very competitively, but used to play it way too often with my brother and swarms and swarms of bots. I remember practicing on wide open maps by giving the bots only knives and myself only scouts and trying to kill them all with as little bullets as possible.
When I go back to try and play it now I'm fucking awful, which might be better as I'd rather still remember it when I was 14 or 15 and actually successful.
Far Cry 2
This game gets a ton of flak on forums and the internet in general, but I loved every minute of it. It's still the only open world game I've played where I genuinely felt in danger of dying or getting injured at every corner. It's also the only non explicitly tactical shooter (Rainbow Six, etc.) that I could really apply tactics to. Every 4 man guard post felt like an different challenge, and even 4 enemies could put you on the ground if you went in guns blazing without scouting the area at all. The quickly respawning checkpoints and hostile AI was annoying, but it didn't detract from my experience as much as it did from others and it's still one of the best shooters I've played.
Call of Duty 4
I feel like a lot of people dismiss COD4 as crap just because of MW2, WAW, and Black Ops using the same engine and not changing the gameplay much at all, but Call of Duty 4 was pretty revolutionary. It pulled off the Michael Bay style campaign like no other game had done before and the multiplayer, even with its issues, was still fun, even by yourself. I bought COD4 on release day and played the campaign to death before I even really realized there was a whole multiplayer component to go along with it. Yes it was heavily scripted, yes the story was shoddy, but it pulled me in like no other shooter had done before.
Battlefield 2
This was, and might still be one of my favorite games to play with friends. Teamplay was fantastic, gameplay was fantastic, and the maps scaled were like no other game I remember. It was also one of those games where you could go 2/14 on KD ratio and still be at the top of the scoreboard, something I really enjoyed as I often went 2/14. Also, Wake Island. So much Wake Island.
Flight Simulator 2002
This was pretty integral to my gaming experience as a kid just because my parents wanted me to get into aviation. It's also the only game I've ever played where you can buzz your own house in an F-15. I probably spent about 30 minutes with the stock airplanes and then rushed to the internet to get addons and extra scenery.
Lego Island 2
Scoff at this all you want, but I figured I had to put it in because of how many hours I sunk into it as a kid. Similar to Flight Simulator, I liked it because you could pretty much run around and do whatever you wanted. Note that this was far before I was old enough to know about the GTA games, so this was really the first "open world" game I ever played. It also had some of the best minigames (Jousting and the cannonball level) I've seen in a game, as well as the worst. (That fucking fishing hole).
Fallout 3
This is on here purely for the sheer amount of hours I have invested into it. The open world was so detailed you could spend hours just running from place to place, not even caring about the storyline (until the radscorpions got to you). I just remember running from area to area and admiring the amount of detail put into the areas, as well as places I know of from current Washington DC faithfully recreated in post-apocalyptic fashion. The combat was beyond janky, but it's always worth noting when a game allows you to decapitate people with a 9mm pistol in slow motion.
Left 4 Dead 2
I'll always remember Left 4 Dead 2 as the game that got me into what I consider "social gaming". I still have never had as much fun with a game as when me and 3 friends were running around decapitating zombies while carrying a conversation about politics or girls or whatever. The game isn't perfect, but it's the most fun I've ever had in co-op. I still always recommend this game to friends new to Steam just so I can play it again, as it's gotten a little boring now.
Phew. That's quite a list.