Wrestling tends to avoid this, due to frequent Heel Face Turns (and Face Heel Turns) as well as the fact one of the most common ways to make a tag team is to pair wrestlers who know each other well, be they friends or not. There are quite still a few, most notably:
Mankind, he and Taker fought in the most violent match in the history of WWE. As Pro Wrestling Illustrated so eloquently put it: "Mankind did more than beat The Undertaker in a match - he changed his very essence."
Shawn Michaels, the rivalry that changed history. He fought Taker in the first ever Hell in a Cell, a Casket Match, a World Championship match, and twoWrestleMania matches.
In the fandom, WrestleCrap and Kent Jones (their Message Board went as far as to filter Kent Jones' name as "Can't Shoot," "I like tired fads," etc.). They also hate 420Chan's /wooo/.
Due to pro wrestling's nature as a staged sport, as well as the close bonds of trust most wrestlers have with one another (putting their lives in each other's hands), many of the cases listed here (not all) are actually good friends in real life, with a great amount of respect for one another. Even Bret Hart and Shawn Michaels, whose real life rivalry was as legendary as any staged rivalry in the sport (before they finally buried the hatchet), expressed tremendous respect for each other's skill and ability, while personally despising one another.
WCW to WWF and ECW, for stealing stars from both feds, the cruiserweight divsion idea from ECW and almost putting the WWF into bankruptcy. Paul Heyman who was fired from WCW fostered this with both the wrestlers and the fans. ECW and WWF were somewhere between Worthy Opponent and Friendly Enemies.
Survival Tobita's was Ken the Box, the one monster he could never defeat. This is because Ken is played by a guy in a cardboard box and has limited mobility. In fact, he can only throw punches. It also meant that he couldn't be knocked down.