I think, for me, I fall into the hipster mentality trap of "I got that game before it became cool." Seeing those red or yellow borders screams, "Hey, everyone else likes this - you should, too!" but that's me, haha.
If anything, I do like to have the "definitive" edition of something though. Sometimes that's the Game of the Year Edition or something that comes out years down the line. More and more enhanced versions of games are coming out, too, so that tends to make the originals less desirable. Tokyo Twilight Ghost Hunters: Daybreak Special Gigs, for instance, will be out soon and might make the original obsolete. Persona 3 FES is the one to have now, though I am happy to have my both my original Etrian Odyssey 1 and EO Untold.