Since most wrestlers theoretically have little say on who they either fight or team with, an Enemy Mine often occurs when an on-screen authority figure randomly decides two people who don't like each other will team up against a common enemy. This used to happen all the time with "Stone Cold" Steve Austin and The Rock. An example would be when Stone Cold was booked to fight The Undertaker and Rock against Triple H at Over the Edge 1999, one Raw saw Austin and Rock being forced to team together against Undertaker and Triple H. Since Undertaker and Triple H were members of the same stable, the story of the match was whether Austin and Rock (who only weeks earlier were in a bitter feud) could put up with each other long enough to survive.
This specific Enemy Mine would occur several times through 1999, not all of them being in official matches. For example: the SmackDown pilot in which the CorporateMinistry came together in the first place.
Stone Cold and The Rock would continue to find themselves unwilling partners as late as 2002, when they teamed up the week before WrestleMania X8 to face the New World Order in a handicap match. By that point you could argue that Austin was Rocky's most frequent tag team partner behind Mick Foley.
Pro Wrestling tag-team title belts can also serve from an Enemy Mine, as a face and a heel are thrust into a match with the titles on the line, and despite their bickering and contempt for each other, manage to win. They're then obligated to continue teaming to defend the belts, arguing and taking potshots at each other all the while, until one of them finally decides being a champion isn't worth the headache and turns on the other. A 2007 example is Matt Hardy and Montel Vontavious Porter on WWE SmackDown!.
Slightly subverted in 2008 with John Cena and Batista, who won the tag titles but were bitter enemies facing each other, and couldn't co-exist, and lost the tag titles back on their first defense the next week.
Even more so with Cena and The Miz who couldn't co-exist as tag team champions for ten minutes before Miz betrayed Cena.
As an interesting side note, all four of John Cena's tag title reigns in WWE have been with enemies or rivals, and each one was shorter than the last as a result. His first World Tag Team Championship reign with Shawn Michaels came during the lead-up to their Wrestlemania match and ended the night after that event, bringing their total reign to 63 days. His second World Tag Team Championship reign was the aforementioned reign with Batista, which lasted seven days. He later won the WWE Tag Team Championship with David Otunga as an unwilling member of The Nexus, losing the title the very next day. His final WWE Tag Team Championship reign was the one with The Miz mentioned above, lasting about ten minutes.
Hilariously lampshaded in a backstage segment with Team Triple H at Survivor Series 2007. Kane, Jeff Hardy, and Rey Mysterio call out Triple H on his numerous past offenses against them, which "the Game" sheepishly apologizes for. However, the team acknowledges that while they don't necessarily like one another, they like the other team even less.
CMLL's Torneo Increibles de Parejas, Arena Puebla and Torneo Nacional de Parejas Increibles all require all teams who wish to enter them to be composed of technico and rudo.
The American Wrestling Association had an angle in 1985 where the Russian faction of Boris Zhukov and Chris Markoff injured Rick Martel. Martel's friend Mad Dog Vachon came looking for revenge and turned to the only man he felt was dirty and ruthless enough to stop the Russians: his old enemy Nick Bockwinkel.
WCW had the Lethal Lottery, a competition made up of tag teams who didn't like each other, the winners getting to advance to the Battlebowl battle royal where they could beat each other up with impunity, giving them some incentive to win.
In a interesting twist, The Rise and Fall of ECW showed that the Tazmaniac and Sabu hated each other in real life, but ended up becoming one of the company's top tag teams prior to Sabu bailing on the company before The Three Way Dance on April 8, 1995.
During the first Los Independientes attack on CMLL in April 2010, CMLL regulars Averno, El Texano Jr and El Terrible took the opportunity to blindside Brazo de Plata, Místico and Jon Strongman when they ran out try and save La Sombra, El Hijo del Fantasma and La Máscara from the independent circuit invaders.
Subverted at SummerSlam 2010, when usual Cena rival The Miz tried to play on the "need" for this (especially after Cena honestly tried to keep them together, but Edge and Jericho proved incompatible) to make Cena beg him to round out the team... by the time Miz tried to pull the trigger, Cena declared that Miz had taken too long to make up his mind and that Cena had found someone else who said yes first: Cue the triumphant return of one Daniel Bryan.
Team Hell No is a great example, with Daniel Bryan and Kane being forced to enter anger management together, hug out their aggression in the middle of the ring, and become a tag team. They won the tag team titles completely on accident, and they both would spend most of their time bickering and arguing, which through sheer luck would lead them to win after win.
Often happens in Royal Rumbles and Battle Royals, as many wrestlers team up to eliminate the biggest wrestlers.
In the Mexican EAW, London and Kendrick teamed up with their long time rivals, The World's Greatest Tag Team over Marco Corleone harassing Charlie Haas's wife Jackie and London and Kendrick's then third partner, Reby Sky. Corleone had backup from El Hijo de Rey Misterio and Zach Gowen so they needed the numbers to avoid more inter gender matches.
Pretty much enforced by Madison Eagles and Jessicka Havok on SHIMMER Volume 70, who were on separate paths of revenge against Nicole Matthews and Portia Perez, met up, and took the Global Green Gangsters along with them.
In January 2015 at the IWC Reloaded event, the first show under a new owner based around a randomizing "reset button" gimmick, Joe Rosa & Jimmy Vega$, members of rival power stables Faces Of Change and Founding Fathers, as well as personal enemies, won the tag team titles and had to be threatened with suspension to agree to act civil afterwards. At the same event, John McChesney and Jimmy Nutts teamed up against Team Big League for interfering in their match, McChesney presumably being a former member of the group from then on.
In the World Wrestling League, Savio Vega had been determined to see Heavyweight Champion Glamour Boy Shane fail, with President Richard Negrín sending out former champion Monster Pain to ensure Vega stopped messing with Shane. But Shane came to Vega's aid at the 2015 Guerra De Reyes event when Negrín fired Vega and then formed "The Gentleman's Club" with Escobar, La Amenaza Bryan, Joe Bravo, Hiram Túa and freshly crowned Heavyweight Champion El Patron Alberto, who all beat Vega bloody.
Enforced at WWN Live Mercury Rising 2015, where Mia Yim and the Kimber Bombs were set to take on The Canadian Ninjas and Nikki Storm. Andrea of Valifornia ran out and beat Storm senseless while stable leader So Cal Val informed Portia and Nicole that Andrea had replaced Nikki.
During the Fourth of July Raw in 2016, there was a Team USA vs Team World match that is notable for one reason: Kevin Owens and Sami Zayn competing as a team in WWE for the first time. (Of course, they had a history of this on the indies as well)