The first shooter game that I remember using dual analog sticks for was Red Faction on the PlayStation 2. I never did play it all the way through, but I knew the demo backwards and forwards. To me it was a big advancement of the Nintendo 64 joystick and C buttons, which I'd previously been accustomed to from playing hours upon hours of Turok 2: Seeds of Evil and Goldeneye.
When Red Faction II was released, I didn't have much of a choice but to buy it immediately. I was upset that it lacked online play (SOCOM: US Navy SEALs and Tribes: Aerial Assault were the hot, new online items for PlayStation, and Xbox Live had already launched), but being able to makeshift some co-op play against bots a la Unreal Tournament was the biggest selling point for me. That, and Geo Mod.
After playing through the campaign - which could have used co-op, by the way - I started having fun with the splitscreen multiplayer. Eventually I realized that bots could be customized, and even saved to memory cards. A couple of months went by, and as new games hit store shelves Red Faction II was somewhat forgotten. It would be revived, however, when a good friend and I decided to venture from home and become apartment roommates - as it turned out, he also enjoyed Red Faction II and had saved custom bots to his memory card.
Imagine spending several hours honing your very own AI team and leading them in a deathmatch against your friend and his AI. Now, imagine teaming up against eight AI players that are statistically almost as experienced as you are.