Rocky V

Probably the most compelling fight scene in the whole Rocky series (aside from the new one, which I haven't seen yet), is the final fight from Rocky V. Its a street fight between Rocky and his former pupil Tommy Gunn.

Basically, the fight scene isn't Rocky vs. some ridiculous stereotype or just general all around crazy person. Its a person who you actually know, and have made at least some small connection with through the course of the movie. Granted Gunn is an all around jerk to Rocky, and thus deserves to get his ass beat, but you, as the viewer, still have a connection with him. For the first 4, pretty much all you saw of the adversary was a training montage, and the pre-fight press conference. So, basically, you had an over-the-top Carl Weathers for 2 movies, Mr. T and Dolph Lundgren for the other 2.

And the 5th one was the one that didn't follow the same formula as the others. Namely: Rocky has some sort of challenge, starts to train, kind of sucks at it, and then Adrian shows up, he starts to train much better, and then eventually prevails in the fight.