To get more into some of my attachments:
When I was a child, before preschool even, my parents got an NES. My dad primarily played Duck Hunt, but my mom and aunt played Super Mario Bros., and I just watched for most of this time because I was absolutely terrible. Eventually, my mom's friend let us borrow (and eventually keep) the original The Legend of Zelda. I watched my mom play it hundreds of times. I'd watch, I'd get flinch and yell with her when she got hit/died, I'd get excited when she found a new item/beat a dungeon/found a heart container. It was great. I watched my mom play a lot of games, including Castlevania III and Dragon Spirit. Eventually, I started playing games myself, and we started playing co-op games, like Ikari Warriors and Teenage Mutant Ninja Turtles II: The Arcade Game. But the fondest memories were still of Zelda, which I eventually dedicated time to trying to beat for myself. And the biggest accomplishment came when I found the Red Ring in Level-9. My mom hadn't. She beat the game with the blue tunic. I was beside myself when I found that AND beat Ganon. I had surpassed my mom in Zelda. Years later (as in, when the Collector's Edition came out), I finally wound up getting 100%, and then replaying through the 2nd Quest, which my mom usually stopped during.
Unfortunately, we skipped SNES in favor of Genesis, so an entire generation of memories was replaced with she and I playing Sonic 3, Sub-Terrainia, Jurassic Park: The Lost World, World of Illusion w/Mickey & Donald, X-Men 2: Clone Wars and Castlevania: Bloodlines. Now that I was older, and able to play these games (and the Genesis was mine), it became more competitive. We would try to best each other. She worked at night, so I'd be at school, while she played, and then I'd come home and get further on my save or my run. But we'd also share info with each other on how we did things. This also occurred with Link's Awakening, but neither of us beat it originally because we got stuck at stupid parts (someone also stole our copy of the game, and I wound up getting another copy a few years later, where someone pointed out the stupid detail I was overlooking in the 6th dungeon that stumped me).
This continued on until we finally got an N64, with Ocarina of Time. Same deal (took turns, she while I was at school, myself when I got home, and we'd try to pass each other). I'll never forget how awesome it was to beat Ocarina of Time. Ah man... Unfortunately, after that, she didn't really have time to play anymore. She didn't really like the time mechanic of Majora's Mask, and she didn't like the sailing in The Wind Waker, and she stopped playing Twilight Princess because I got frustrated watching her and I was backseat gaming. She did end up playing through Phantom Hourglass, and seemed to enjoy it, but that was the extent of that.
So a bulk of my childhood was playing games with my mom, and the only Nintendo games actually happened to be Zelda ones and the original SMB (but none of the others until Sunshine). Now, I had played Metroid, Kirby, other Marios, etc at friends' houses and at a thing I went to during the summer, but it wasn't until Pokemon that I actually delved into another Nintendo franchise myself.
Then Super Smash Bros. was announced, and holy crap. I literally cared about nothing except for the fact that you could play Link. I was freaking out. I was at Weis with my mom, grocery shopping and I looked at a Game Pro or XpertGamer magazine or something and see screenshots and flailed. I begged my mom to buy the magazine JUST because it had that single page with a few pics of it.
It was also the first fighting game I had ever owned, so the concept of beating it in like 10 minutes was totally beyond me and I was very confused when I beat Master Hand, but man... that game changed everything.
I only played Link, and to a lesser extent, Ness & Captain Falcon. Neither of whom I knew. I was completely confused by who these characters were.
I also proceeded to have my mom buy at least two other magazines that had SSB in them. One had info/preview stuff that showed all the starters and had all the games they'd been in up to that point, while the other was a vague guide that revealed how to unlock everything and how to beat their Break the Targets/Board the Platforms. I also became THE friend to hang with, and I was everywhere, bringing the N64 and/or SSB and controllers. My friend & I even created a rivalry out of Link & Samus, since those were our characters, It was great.
And to think, that only a couple years later, Melee came out. Which I was grounded during, so I had to play in secret, and play at my friend's house.
Instead of veering off for the rest of my life over the course of that time (in this post, anyway), I just want to focus quickly on the fact that Melee really made me stop to consider "Maybe I should play some of these other series..." and I got F-Zero GX, Super Mario Sunshine, Metroid Prime, Kirby Air Ride, and so on. Buying these games prompted me to play other games in the series that I missed (Super Mario 64, Metroid...) and buy an SNES from a friend, with Super Mario World, then get some hand-me-downs of DKC, Star Fox, Super Metroid... and I finally bought ALttP (on GBA).
Fast-forward to now, and I own at least one game featuring every character/franchise in Super Smash Bros. (although, I don't actually own Gyromite, or a R.O.B. game, but I own several games with R.O.B. cameos). In some cases, I own all of them now in some form (digital or retail). And why? Because I love these characters, and it was Super Smash Bros. that caused this. I don't love ALL of them, but nearly all of them. Melee and Brawl got me to try games I never really gave a chance to, and in some cases, I gave a second chance to, after dismissing them, and now I love the characters even more, and their franchises even more, and I can't wait to see them return, or to see some of my favorite faces show up for the first time.
So yeah, characters are a huge deal to me for SSB. They're like family, and new friends.