Pele vs Macaco by a mile - so many incidents during their fights stick in the memory such as Macaco ripping Pele' ear-ring off....or the pair of them stopping fighting for a few seconds and just standing in the middle of the ring eyeballing each other......Macaco showing off with some backflips before the first fight - if you don't know their fights do yourself a favour and check this out for a taste of what you have missed...nothing compares....
http://www.youtube.com/watch?v=b9pYpGJjTUs
Sak/Gracies and Tito/Lion's den because of the longevity of both.
Sak fought Royler, Royce, Renzo and Ryan.
Tito fought Mezgerx2, Kenx3, Frank(doesn't really count) and Bohlander
BTT vs ChuteBoxe
Mma rivalries have been pretty weak with maybe the exception of gsp/Penn and Tito/Chuck.
That being said, Silva/Sonnen has all the potential to be MMA's Ali/Fraizer 
I liked the hughes/penn rivalry.
Arianny vs. All other UFC ring girls
PembrokePinesVillain -CRBMoney14 - No Chute Boxe/Hammer House?
this.
seemingly most violent
UFC v NY
HYBRID JON - Barnett/ Dana White
LOL
Too bad Barnett backed down..
FUTA vs. Fudd
Beat-Your-Boss-Boxing match. Fudd got fuckin SWOLE of the HRT and hasnt looked back!
crazydave - TITO and Chuck.
Mark Coleman vs The Ropes of Pride after the Grand Prix.
In a fleeting moment - Cal Worsham vs the top of the cage, trying not to get chucked into row 3.
Me vs My Comp. Trying to find a broadcast that carried Pride before it was on PPV. I'm actually surprised I don't know more Japanese than I do. I still remember listening to Sak vs Royce at 3 AM. That fight took forever!!!!
But as for rivalries - I offer you JIM BROWN vs the Ring Girls. The struggle JB was in to try to not MOAN every time they walked by was obvious - and he generally went ahead and moaned anyway.
Can't believe no one mentioned:
Fedor vs Big Nog
No trash talk, but emotional, Nog was #1 HW @ the time, got stomped but had the heart of a lion. He was like a real life Rocky 1, but never pulled off the upset down the road.
Tito vs Lions Den
roiding mma fanboys vs. the all natural badass MONEY MAYWEATHER
Chute Boxe vs BTT
Some real hatred between those camps at one time.