In Kane's second most notable tag team, with The Big Show, Kane played the Blue Oni to Show's Red. Kane tended to be the more stoic (if psychotic) of the two, while Show ranged anywhere between Hot-Blooded to Big Fun.
Maybe during their initial run, but after going singles, Edge is a much wilder, crazier Red, and since his return, Christian is a calm, relaxed Blue.
Former WWE Unified Tag Team Champions Mike "The Miz" Mizanin (angry Red) and John Morrison (mellow Blue).
The Rockers (originally AWA's Expies of The Rock N Roll Express from the NWA), Marty Jannetty (Blue) and Shawn Michaels (Red); notable for the fact that the group originally split after they gradually switched roles over the course of their 5-year tag team career.
In the same vein, the most recent iteration of D-Generation X, with Shawn Michaels back in the Red Oni role and partner/best friend Triple H in the Blue Oni role (it can also be noted that Hunter can switch the colors pretty much on demand now as a story needs him to).
On that token, "Rowdy" Roddy Piper lived up to his moniker when he served as Monsoon's replacement Red with Brain.
The APA was a good example with Bradshaw as the Ranting Red and Farrooq as the Blue of a single word. That word, of course, being "DAMN!"
In TNA, you have Mr Anderson (rule-breaking, stubborn asshole Red) and Matt Morgan (higher-minded, honourable Blue), although, in an ironic twist, Anderson's entrance lighting is very blue-themed whereas Morgan's is very red.
Raw and Smackdown are this right down to their colors. RAW has more crazy segments and is most of the time aired live while Smackdown is usually geared towards wrestling and is always taped.
Legendary All Japan Womens Pro Wrestling tag team the Crush Gals: Chigusa Nagayo (Red) and Lioness Asuka (Blue). Neither fell into the absolute territory but Nagayo was usually the more emotional, passionate one while Asuka was the cooler, calmer one. They even wore red (for Chigusa) and blue (for Asuka).
MsChif is the Red Oni of MSEERIE, where her partner is the comparatively quieter and less outlandish of the two and the Blue Oni of Diabolic Khaos where she is the comparatively subtle strategist while her partner runs around wild hitting people with foreign objects while babbling about random topics.