I know that for me, the DC was really the beginning of me being... I don't know if "hardcore" is the right word for the situation... "passionate" is more appropriate. It was a turning point in how I viewed, played, and felt about gaming. A religious experience? Hahahah.
I didn't start using the internet seriously until late 1998 or so, so throughout the whole 5th-gen console era I was largely oblivious to jaded gamer hype, tell-all pre- and reviews, and console wars outside of the microcosm of my circle of friends. Now that I was "on-line" I was able to suckle at the teat of internet discussion groups (repping the newsgroups rec.games.video.sega, nintendo, sony, and other smaller boards) and feed off the hype machine.
DC was the first console I pre-ordered, before this I wasn't so hyped that I NEEDED to have a console at launch. (Ok so maybe N64 was like that, but only for Mario 64.) I picked up
Sonic Adventure and
House of the Dead 2 (and a light gun of course!) with it, and kind of got into my current game-consumption habits, rolling through about 2-3 games a month.

Between the PSX reaching its apogee and DC's release I was buying like 5 games a month at this point, haha. Within the launch months I eventually got
Soul Calibur, Sega Bass Fishing, Sega Rally 2, Marvel vs Capcom, AeroWings, Armada (I was WAY too hyped for this game), Evolution ... damn now that I look back didn't the DC have one of the best launches/opening months ever?
In addition to all those that I owned, through friends and renting I remember playing
Slave Zero, Mortal Kombat Gold, Hydro Thunder, Toy Commander, and way more I probably can't even remember. All in those first few months!
I have some more to reminisce about, but I think thats a good starting point, haha.