My sealed collecting started with Dreamcast actually, after the console had "Died" and games were widely available sealed, cheaply, on eBay. I was also picking up sealed N64 and PlayStation games cheap around this time as well (Circa 2002)
I started buying PS2 games before I got the console in 2003, and many I opened until I bought Space Channel 5 Part II which was my first PS2 game I kept sealed because of its rarity in this condition. I would open a handful of games to play, but most stayed sealed due to lack of time to play everything I was buying.
I also bought a GameCube and Xbox at the same time as a PS2, and likewise many of my earlier games I opened to play. As with the PS2, I only really started keeping them sealed due to no time to play anything. I think Steel Battalion Line Of Contact was the first game I kept sealed for the Xbox
N-Gage games I started buying and playing, until someone I bought a game off on eBay sent a Cd-r with every game on it, so I then decided to keep these sealed, but still bought them. The appeal of collecting N-Gage games is that there were only a few dozen in total, so it's a small collection to collect.
GBA games I decided to start keeping sealed around the time Minish Cap was released, and around the same time I discovered VisualBoy Advance...
What started out as just harmless backlogging turned into serious anal OCD. It got to a point where I was deliberately collecting sealed games, rather than storing them until such time I wanted to play them, which was how it started. I find i'm buying more than I can ever possibly play, but don't see why I should give up collecting games, and it makes sense to leave them sealed until such time they are intended to be used. My OCD has spanned across into other mediums now as well, including Dvd's and Cd's
Fast forward to present day and my entire X360, DS, PS3, PSP, and Wii collection's are sealed (With the exception of Wii Fit and Link's Crossbow Training which are new and unused)