There have already been a couple glimpses at what would be considered boxer vs. martial arts style fighting, and neither made boxing look good. 
One occurred all the way back at UFC 1 in 1993. Art Jimmerson was a light heavyweight with a solid record of 29-5 when he squared off against Royce Gracie. Gracie needed all of 2:11 to pick Jimmerson apart. From that point on, Jimmerson went 4-13 in his boxing career. Word got around boxing quick to stay away from UFC.
OK, maybe Jimmerson isn't a big enough name to impress you. How about Muhammud Ali, then? 
Back in 1976, Ali took on wrestler Antonio Inoki in Tokyo. They went 15 rounds before the fight was ruled a draw. Inoki spent most of the fight on his back in a basic jiu-jitsu defensive posture and repeatedly kicked at Ali's legs. Ali's punching was useless, as he threw just six punches the entire fight.
It was a dreadfully boring exhibition by all accounts. But no less an authority than Thomas Hauser reported in his definitive biography Ali that Inoki did so much damage to Ali's legs, that Ali had to be hospitalized with blood clots and extensive muscle disrepair. Promoter Bob Arum went on to speculate the beating helped speed up Ali's in-ring decline.
So there you have it. Three decades before MMA stole boxing's thunder and 17 years before Gracie burst onto the scene, the greatest boxer of all-time could do nothing against a professional wrestler who used defensive martial arts tactics that were primitive by the standards of today's MMA.
Here are some Boxers that have had success in MMA! 
There have been two boxers to cross over with success that is Marcus "The Irish Hand Grenade" Davis Who has Recent wins over Shonie Carter and Pete Spratt… Also Jeremy Williams (boxer) He recently fought successfully in Icon Sport on the Trigg vs. Lawler under card! He is 3-0 in MMA with two submission wins! Check out their stats below!
Marcus Davis wikipedia http://en.wikipedia.org/wiki/Marcus_Davis Jeremy Williams wikipedia http://en.wikipedia.org/wiki/Jeremy_Williams_(boxer)
The History of Boxers in MMA
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