Unequivocally and without hesitation, the third season is my favorite season of Buffy. After a great second season with lots of Spike, season three really solidifies the series for me. And there are such great characters and episodes.
Faith is new to Sunnydale in season three, and immediately is the anti-Buffy. The friction between Buffy and her new, soon-to-be evil counterpart is great to watch. Seeing Buffy watch and try to experience the life she could have had creates more depth in her character and brings Faith to the forefront, setting her up for some great episodes to come.
Oz is also one of the great characters of season three. He appeared in a few episodes of S2, but he really became a Scooby once he really started dating Willow and coming into his own werewolfiness.
Mayor Richard Wilkins III. What more can I say about this Big Bad? Once the seedy underbelly of Sunnydale revealed that the Mayor was more than just the Mayor, it created a whole new game for the Scoobies.
Other than characters, there are some great episodes. Band Candy, The Prom, Graduation Day and Dopplegangland come to mind.
Also, in my mind, season four was transitional, therefore season three was the last of the stability the Scoobies will have ever had.