Probably the late 90's -early 00's for several core reasons:
1) Getting together with friends for massive gaming parties. We'd either be all gathered around a N64 playing games like Smash Bros., Goldeneye, Perfect Dark, and Mario Party or bring all of our PCs together for a full on LAN party with games like Starcraft, GTA II, Delta Force, or Rise of Nations.
Granted, me and my buddies still do game nights, but we've drifted more to card & board games, so a round of Catan is more likely than a round of Halo (though we do always set some time aside to play some of the genuinely terrible titles in my collection.
2) The lack of responsibility. Back then, as a kid, I could just sink hundreds of hours into my games, without a general care in the world. My core time sinks were probably Smash Bros., Civilization II, TIE Fighter, Starcraft, and Pokemon. Nowadays, as an adult with a full time job, progression through my backlog goes very slowly.
3) Piracy. Back in middle school, I was made aware of emulators and ROMs. All of a sudden, I had the entire NES and SNES library at my fingertips, and I made use of it, basically trying every game I could, just because I could. This broadened my gaming horizons so much as I was encountering gems I would've missed otherwise on my kid budget of 4-5 games per year (plus Blockbuster rentals). I've long since gone legit, as once I got a job, I enjoyed buying the games more (especially as I could see them on my shelves), with the only downside being that my purchasing speed has greatly outstripped my playing speed.