What DBZ fight lasted a whole season? I've heard that Dragon Ball Z once stretched a fight (sometimes they say one punch) over most of a season.

Which season was it? What are the episode titles? How did they do it, were there flashbacks or cut-aways, or constant fighting?
The Frieza vs Goku battle lasted from the time Vegeta dies to the explosion of Namek spans in episode 87 to 105, the infamous "five minute" battle itself starts at episode 97. 

The fight between Goku and Cell at the Cell Games starts at 177 to 180 and Gohan's fight with Cell begins at episode 181 and ends at 191.

The final battle with Buu spans from episode 279 to 287. This is the most varied battle out of all of them.

So technically, the battle between Frieza and Goku is the longest and most drawn out battle between two characters.