My general collection habit started with the first system I ever owned - the Intellivision. My dad had it from when from when it first came out, and while we waited to get an SNES we had it. I got a chance to experience old-style graphics and highly point based gameplay even though by the time I was able to play, it was the SNES/Genesis generation. Every now and then he'd bring home new games from the flea market, and me and my brother would play Frog Bog, Night Stalker and Astrosmash for hours. I got my SNES eventually (Which, to be fair, also contributed a large part to my urge to collect) but the Intellivision always fascinated me. From then on, older systems where always a mystery to me. For example I could never get much NES playtime due to my daycare's NES constantly blue screening and that has been a major contributer to my NES collecting.
Also, my family has always been one of collectors. My dad collected all sorts of things, we have a two-story garage packed to the brim with random stuff, but mainly he collected coke bottles, and had a room full of them equivalent to what I have to games today. I was always collecting something (Pogs, Beanie Babies, Pokemon Cards, etc.) but Video Games is the one I stuck with.
I also really love the functionality of a video game. It is more then it's physical appearance compared to most knick-knacks. For example I have Earthbound, which is (annoyingly) becoming a collectors item, but I bought it because it was Earthbound (luckily before it became as pricey as it is now.)
Anywho, that's perhaps a little too comprehensive, but there is my answer.