Sonic 3 and Knuckles is my favorite, plain and simple.
I admire how fun it is to play, and just how SOLID it is. The levels are pretty large, there are unique paths for different characters, and you can have a slightly different, but still fun experience each time you go through it. It's like the Super Mario 64 of Sonic games.
Honestly, Sonic 3 and Knuckles really is a timeless game. It LOOKS great, it SOUNDS great, it FEELS great to play. It's a flawless Sonic game, and I'd play it over and over for years to come. I just love it.
Another thing that I like about Sonic 3 and Knuckles, although it's technically an entirely different game, is BLUE SPHERES. Blue Spheres is my favorite special stage in any of the Sonic games. It's both very simple and yet very challenging at the same time, and I absolutely love it. I feel so proud of myself trying to master the frame-perfect turning in certain aspects. It's just riveting.
Overall, I'd give Sonic 3 and Knuckles a 10 out of 10. It's an absolute gem, and it's a complete shame that it hasn't been properly rereleased on any modern consoles other than Wii Virtual Console, which is what I myself have and play Sonic 3 and Knuckles on anyways.
Sonic 2 is fun, but I mostly prefer the 2-player aspect when playing it with my younger sister. For whatever reason, in both Sonic 1 and 2, I can't bring myself the effort to complete the entire game in one go. I never have the patience. This is why I admire Sonic 3 and Knuckles' save feature.
I know I'm a little biased toward it, but I've played S3K for over 10 years, and I have very fond memories. I enjoyed it as a kid, and now that I'm a little more mature and better at it, I enjoy it even MORE now! :)