My favorites are the Advanced seasons. (Pokemon Advanced/Challenge/Battle, Battle Frontier)
There are so many things I love about the Advanced season that I couldn't list them all without filling up the page.
(But I'll try to list some anyway)
~The season's during the third generation of Pokemon. (my favorite gen)
~Most of it takes place in the Hoenn region.
~The art style of the entire series changes. It looks smoother and better. (Like the new style of Sugimori art for R/S)
~The opening songs are awesome. (Advance Adventure/I wanna be a hero)
~I like Ash's new, advanced clothes.
~I like a lot of the episodes. (even if the majority are fillers)
~A lot of Ash's Hoenn Pokemon have very distinct personallities.
(I know that his older Pokemon had different attitudes as well, but it seems to stick out more here. Possibly because of natures in R/S?)
~The season started a lot of contreversy about Misty. New PokeShippings also spawned with the apperance of May.
~The series makes a big change with Ash leaving all but one of his old Pokemon behind, and joining up with new characters.
~Ash gets his Treecko. Enough said.
I don't like the BF season as much as the Hoenn seasons (only a little), but it's part of the Advanced series anyway.
(A majority of my favorite episodes come from the BF season, actually)