Kirik -
I have been punched in the face by Jorge Rivera who has been punched in the face by Anderson Silva. 2 degrees of punch separation. How close are you to some of the greats?
I got punched by Cole Escovedo who got punched by Jens Pulver who got punched by BJ Penn 
If you've done any amount of travelling and been in the game for a while, this could quickly get boring:
4 degrees from Fedor.
3 degrees from Cro-Cop.
(plus every fighter that the above two imply).
3 from Robbie Lawler.
2 degrees from Hideo Tokoro (twice - one training partners and 1 opponent in different countries).
2 from Takanori Gomi.
2 from Hector Lombard.
2 from Anthony Perosh.
2 from Brian Ebersole.
2 from Kid Yamamoto.
2 from Joey Villasenor.
2 from Ninja Rua.
2 from Eddie Alvarez.
2 from Gilbert Melendez.
2 from Bra Pickett.
1 from Che Mills.
1 from Marius Zaromskis.
1 from Shinya Aoki.
1 from Masanori Kanehara.
This is a fraction. I'm bored and will stop now. Pro MMA fighters could spend all night compiling this type of list.
Worked out with a friend, who was trained by Floyd mayweather sr who fought sugar ray Leonard who was trained by Angelo Dundee, who was also Cassius clays trainer. He fought George foreman, who fought Evander Holyfield who in turn fought James toney who "fought" randy couture....that goes everywhere.
MinuteMan1979 - I've been punched by Frank Dux, who was punched by Bolo Yeung, who was punched by Bruce Lee...
i was patted on the back by chael sonnen, who patted on the mat to anderson silva? and shook the hand of dfw (at the ug meet and greet!) who shook up the world of mma for every mma fighter ever! (does this count?) 
I got punched in the ribs by a guy who fought a guy who claimed to have been punched by BJ Penn. So, 3. Not bad, but it's Hawaii so shrugs
I also got drunk a lot while living in Hilo, so who knows, maybe a smaller degree I don't know about. Got punched quite a few times being an idiot.
was punched by Kyle Kingsbury who was punched by Jimi Manuwa
I've been punched in the face by Kenny Florian which puts me a degree away from BJ Penn.
Tom Lawlor -was punched by Kyle Kingsbury who was punched by Jimi Manuwa
The 2 degrees of UGrs.
rodhicks - I've been punched in the face by Mike Bruce who has been punched in the face by Travis Fulton. I'm 3 degrees from every fighter ever
Lol, true
I got a slight punch in the shoulder from George Chuvalo after one of his presentations at my school per my request to get punched by one of the greats.. I think he got punched by Ali a bunch =]
I trained under a guy who trained with Rick Legere who lost on TUF to the Manley guy, so I am pretty much Forrest Griffin
StevetheWeasel - OK.
I beat Dan Swift, who fought Phil Johns, who fought Shonie Carter, who fought Steve Berger, who fought Jeremy Horn, who fought Dan Severn, who fought Oleg Taktarov, who was in Predators with Laurence Fishburne, who was in Mystic River with Kevin Bacon.
Nice
But a better one would be I sparred with a guy who trains with Josesito Lopez and Chris Arreola. So with just a couple degrees of separation I have been punched by Victor Ortiz, Canelo Alvarez, and Vitali Klitschko.
Been hit numerous times by ed bavelock, who has coached and been hit by Brian ebersole, who's hit lytle, who's hit Hughes, who's hit Penn/GSP.
I'm basically a contender for P4P goat.
If I got hit in the face with my own camera because I got too close to a sparring match, does that count?
Edited: If yes, it was da Mauler dat done it to me...
ObamaCare -lkfmdc - heh heh, this should be fun... I've been punched in the face by both Shogun Rua and Ninja Rua :)
If things other than punches count, was pummeled into mush by Randy Couture and leg locked by Oleg Taktarov...
pics, or none of this happened.
My training partner trains with Manu Ntoh who trains Brian Stann who fought Sonnen, who fought Anderson. So 5 from Silva.