I've played many beat'em ups, but only one has truly warmed my heart. (aka, liked so much I made boss videos of it)
And that's the Streets of Rage series, or in particular, Streets of Rage 2.
That game had such presentation, especially in many of its bosses.
Blahblahblah (Click to reveal)For example, the epic rain effect following the shirt ripping bartender Barbon saying "Come ON!"
Or the flying Jet swooshing past you and coming down to begin beating the crap out of you!
Or even perhaps Zamza coming out from the mist and shadows like a stupid ninja!
OR Mr. X commanding Shiva to fight, which leads up to something epic!
OR Mr. X himself, seeing you defeat his #1 henchman, tossing his cigar awesomely, and getting up, READY TO FIGHT! (This was on the Japanese version btw)
Point is I really liked the boss battles
And of course the music.
I liked SOR 3, but the original version though, because the character colors were kind of ugly on the US version, and the story was weird.
Comix Zone was mad awesome too, as stated on the post above me.