I mainly respect individuals whose collections exhibit some kind of discernable taste, which doesn't apply to the Collect All the Things types most of the time. A friend of mine in NYC has a fantastic collection of games, mostly focused on Japanese platformers and RPGs, and Kimimi here on VGC has an absolutely staggering assortment of Chinese and Japanese games, along with an ever-growing lot of arcade boards.
I'm certainly not starstruck (sorry, Kimimi ^.^), but it's inspiring to see people like them who act almost like curators, carefully choosing what goes and doesn't go into their collections, while people who fill theirs with random crap seem more like compulsive hoarders. Quality over quantity wins out every time.