Some fighters who have had real life vandettas:
-Rich Clementi and Melvin Guillard were reported to have had an altercation a while back and had a pretty heated fight.
-Yoji Anjo once went down to Brazil, to Rickson Gracie's dojo and challenged him to a match, and apparantly Rickson subbed him in minutes in front of several reporters.
-There has been long standing beef between the fighters from Brazilian Top Team and Chute Boxe, with probably the biggest being between Ricardo Arona and Wanderlei Silva.
-Anderson Silva has said some bitter things about his former team, Chute Box and most specifically about Wanderlei Silva. reportedly, they treated alot of their "black" fighters like shit.
-Theres the obvious feud between Tito and The Lions Den which started after Tito beat Guy Mezger and flipped off the whole camp.
-Fedor/Aleks/Zentsov/Kharitonov were once apart of Russian top team, but Fedor and friends thought that RTT was corrupt and treated them like shit, so they got up and left, leaving Sergei behind.
-During Mark Coleman's match with Shogun Rua, Shogun fell and broke his arm, at which time the both camps (Chute Box and HammerHouse) came in and started rumbling and Coleman was somehow seen stepping on Wanderlei Silva's neck. After the incident, they had another altercation backstage and shouted at eachother a bit. After his recovery, Shogun went on to beat Kevin Randleman.
I will think of more soon and add some video.