Absolutely.
I grew up with an Atari 2600 and as soon as I could manipulate that joystick, I was a gamer. For me, collecting games is extremely emotional because I have so many countless memories tied to specific games and systems.
I remember trying to beat that blasted worm room on The Immortal (Genesis), or staying up all night with friends to unlock all the secret characters in Eternal Champions on Sega CD. I remember finding Shining Force CD at a local used record shop for $30, the crushing disappointment I felt when I went into Toys R' Us to discover they were out of Ghosts 'n' Goblins on the NES. I remember selling my NES and all my games to buy a Genesis - the first system I ever bought with my own money instead of a "family" system - and how I regretted it. Not because I didn't love my Genny (it was, and remains, my favorite console) but because I missed playing all the great NES games I had amassed.
I remember being so indecisive over whether to buy NightWarriors or X-Men: Children of the Atom for my Saturn that I ended up just buying them both, and picking up Panzer Dragoon Saga and Dragon Force together off eBay for $225 several years ago (the most expensive gaming purchase I've ever made, but quite a deal looking back).
I remember where and how I obtained tons of games, both console and PC, and I have so many memories of playing them I could write a book.
A house fire nearly destroyed my collection in 2009, and while my carts were lost, amazingly all but one of my disc-based games survived (though the cases and artwork suffered smoke and/or water damages from the hoses). After that, I didn't want to collect for a while, but when the Retron 5 was announced I realized I would need a collection of classic games to play on the console.
As the months rolled on with no release date in sight and I amassed a collection of great titles, I found a great deal on a Genesis, Sega CD, and 32X on eBay - just like I had lost in the fire. I bought it...then I bought an NES...and a top-loader...and a SNES, and so on. I am now 24 games shy of 1,000 titles, and I have them all stored in a spare room in my house, affectionately referred to as the Game Vault. Ironically, I did buy a Retron 5, which had a non-working Genesis cart slot that erased my Phantasy Star II saved game, and I ended up returning it and sticking with the original consoles.
When I was little and saved up for weeks to buy just one new game, I couldn't have imagined having a collection like the one I have today. I feel I am very young at heart, and my love of gaming is a big part of that. I still get so excited when I see my local shop got in a classic game that's on my wishlist, and I rush up there to pick it up, just like when I was little and I'd scour stores that sold used games and find gems for a few bucks.