I love Smash Bros. because it was one of my first video games I have ever played. I remember the Christmas I got my GBA. It was my 1st gaming console I ever owned. Because I got hooked onto that (I think Lego Racers for the GBA as well as a Frogger game and maybe a Casino game were my 1st 3 games), we got a GameCube (I think because we liked Mario Party 4). I then saw a game known as Super Smash Bros. Melee. It was AMAZING at the time (I still play it to this date, but more so just with my friends as I 100%ed the trophies in the game) and it introduced me to many of the franchises that I love to this date (however, I did know several games like Pokemon and Mario at the time). I became an avid Metroid fan because of Samus. I bought F-Zero GX because of Falcon (never beat it as it's SOOOOO HARD). I bought Stairfax Temperatures and eventually Star Fox Assault (as well as the 3ds remake of 64 and the DS game) because of Fox and Falco. I was introduced and hooked into the Fire Emblem series thanks to Marth and Roy. I got EVERY single main series game of Zelda thanks to Link and co. You get the rest. Basically, Smash Bros. helped me become the gamer that I am today. I also appreciate the classic games way more thanks to the series. Also, the gameplay was marvelous.
I eventually got Brawl and I loved it as well. Sure, it might not be as competitive as Melee for tournaments, but it was (and still is) fun for me and my friends. I loved how there was a TON more to do in Brawl content wise. More characters. More stages. More modes. Custom stages. My music. Subspace Emissary (though it can be improved upon). Boss Battles. You name it. Also, it makes a great game to just play for fun and it celebrated Nintendo's History. Tripping, less hitstun, and the abusive air dodging system (which I like WAYYY more than Melee's helplessness inducing Air Dodging system) does hurt it competitively a bit though, but it's pretty good in that regard as well for the most part. So, you can say I prefer Melee when playing competitively and that I prefer Brawl when playing for fun and when playing in Single Player mode (though I enjoyed Melee's event matches a biiiiiit more).
I lack an N64. So, I couldn't get to Smash 64 for a long time. Thankfully, Nintendo eventually put Smash Bros. 64 on the Virtual Console. I've played it and I have to say that it was great for a 1st game in the series. Sure, I enjoyed the other 2 games a ton more, but without Smash 64, we wouldn't have the other two (soon to be 3 with Smash 4 around the corner) games as well as other things like Fire Emblem being localized, Kid Icarus getting a 3rd game, the GameCube selling as many units as it did (Melee was the best selling game for the Cube IIRC), and so on. So, you can KINDA say it's one of the most important games in the Smash series if not THE most. Nintendo benefited from Smash Bros. We benefited from Smash Bros. Everyone [who has played it and liked it] has benefited from Smash Bros.
So, in short, I love Smash Bros. because it helped develop my childhood along with my family and friends. It introduced me to many franchises that I continue to play to this day. It helped me get friends that I will never forget (and still have fun with). And to be frank, Smash 4 is one of the few announced video games I'm looking forward to playing. Besides some of the standard Nintendo 1st party titles, I'm only looking forward to Smash Bros. 4 and the occasional 3rd party title like Mega Man, Phoenix Wright, a good Final Fantasy game, and good indie titles like Shovel Knight and Mighty No. 9.
So, history, gameplay, the community, and how it shaped my social life are the 4 main reasons why I love Smash Bros.