My opinion may be affected by nostalgia, but eh, who's isn't.
For one thing, Sonic Adventure was a fresh take on the Sonic series. It was Sonic's first true 3D platformer. However, many more factors than these makes Sonic Adventure my favorite game.
First of all, this was the first mainstream Sonic game to contain cutscenes with dialogue. This allowed the game to build upon a much more complex story than what was achievable with the classic Sonic games. I particularly liked how they managed to tie in the individual character's stories with the main plot. The story of Dr. Eggman (I mean, Robotnik of course) gathering the Chaos Emerald for the purpose of bringing a chaotic water monster to full power was well told. At the same time, each individual story was interesting in its own right (except for maybe Big. I agree with SomeCallMeJohnny that Big served literally no purpose except to slow down gameplay. I mean, they had to give him a plot device (Froggy) to make him relevant to anything at all in the game). Big cats aside, the storytelling was excellent, and they managed to tie into each other nicely.
Secondly, the gameplay was fantastic. I believe this was the game that introduced Sonic's homing attack, and it's a really useful move in Sonic's new 3D environment. Sonic's levels were designed to be fast, and I think Sonic Team succeeded in this regard. Tails's levels are similar to Sonic's in that they rely on speed, but Tails adds his own abilities to the gameplay (his flight) which helps separate him from the speedy blue hedgehog. Knuckles's treasure hunting mechanic, while different from Sonic and Tails, was enjoyable in its own right. Amy's gameplay wasn't focused as much on speed but more on solving puzzles and avoiding E-100 Alpha (Zero) (and I admit, weilding the Piko Piko Hammer was pretty darn fun). E-102 Gamma was interesting because he brought a new style of gameplay to the series (a style which unfortunately was emulated in Shadow the Hedgehog to a new extreme), and that was the ability to shoot enemies. And this is more story-related, but I particularly liked the idea of one of Eggman's Robotnik's robots going rogue. And finally, we come to Big⦠yep. For some reason, Sonic Team thought high speed fun and treasure hunting wasn't enough, so they decided to add another mechanic: fishing. As a kid, I actually enjoyed the fishing levels, if for no other reason than that they were challenging. In fact, I'll admit that I don't find Big's levels completely useless. However, I can see how people would think that Big's gameplay adds nothing of real value to the game, and I admit it gets pretty repetitive, considering that's also how he fights the boss of his storyline. Yes, you read that last bit correctly. He fights Chaos by fishing. Don't get me wrong, it's definitely a challenge, but fighting Chaos 6 by fishing isn't as fun to me as, y'know, actually fighting Chaos 6.
And finally, we've got the music. This game has one of my favorite soundtracks ever (and this is the part probably most affected by nostalgia). The music was memorable to me, and it fit whatever situation the characters were in. The stage music could go from laid back to high speed adventure, and from natural beauty to mechanical mayhem. The characters' themes fit their personality (even for Big. His theme portrayed his more laid back nature pretty well). Even though "E.G.G.M.A.N." wasn't introduced until Sonic Adventure 2, Robotnik had some pretty darn good music in its prequel.
And that about sums it up. From its storyline to its gameplay, and finally the music, Sonic Adventure has managed to remain in its #1 spot to me after years of experiencing other incredible games. I believe that this is the best installment of the series (followed extremely closely by its sequel), and I say that it is definitely a Sonic game worth playing.