Some ok nominations. However I feel the miller louzon fight is a major prisoner of the moment example. Think the fight is over hyped but I do like at least louzon tried to old something out.
Aoki vs melendez. 
yuki nakai against rickson gracie.
Somewhat on topic.
A few years ago I had a get together at my house for a UFC. I had mostly brazillians over, but only 1 or 2 were up on the sport.
One of the uneducated Brazilian fans said something that to this day, stuck with me.
A fighter was getting his ass KICKED. This brazilian fan said, "if I was that guy getting his ass kicked, I'd just kick the other guy in the nuts as hard as I could, then point like "aaaahhh, I got you fucker".
People laughed, I somewhat did. I quickly advised, "dude, that's illegal, and he'd also get a point deduction".
His reply-"who fuckin cares, it's not like he's going to win anyways. Might as well kick him in the balls so you can say you got him at least once".
After some time, I thought about it, and even though it's totally unsportsmanlike, one time, just one time I'd like to see this happen in an mma fight.
You guys are listing competitive fights.
Fedor was close to even with Bigfoot in the first round. Steering-wheeled the shit out of his neck after getting pickingup and forced BF to go to his own back off of a lift.
Sakuraba/Vovchanchyn was a dead even fight. How was it even close to "hopeless"?!
Mike Bitono is the answer, already stated above.
Neil McCauley - yuki nakai against rickson gracie.
Absolutely!
HELWIG -
You guys are listing competitive fights.
Fedor was close to even with Bigfoot in the first round. Steering-wheeled the shit out of his neck after getting pickingup and forced BF to go to his own back off of a lift.
Sakuraba/Vovchanchyn was a dead even fight. How was it even close to "hopeless"?!
Mike Bitono is the answer, already stated above.
Sir the topic is NOT 'hopeless' but 'most courageous'. Many fights listed in the thread were not at all competitive. Frankly if they are for a certain point in time, that okay too IMO (as with my choice).
Having said that, you have made a good choice yourself to back.
http://www.youtube.com/watch?v=vdKUjbOeKcY
Enson
To me it has to be Enson vs. Vovchanchyn. Enson would rather die than surrender. I had to turn away from my tv. I just couldn't stomach it. Every time I see Enson or hear his name I think of true warrior spirit.
Faber aldo. If I remember right I think Faber had to be carried to his corner between 2 or 3 of the rounds. Because he couldn't walk well. But he still stuck in there and showed heart. Bigfoot got mangled by Cain and held on for awhile. Vera showed a lot of heart vs shogun but not as good of an example I guess 
Big Pun - To me it has to be Enson vs. Vovchanchyn. Enson would rather die than surrender. I had to turn away from my tv. I just couldn't stomach it. Every time I see Enson or hear his name I think of true warrior spirit.
So if the issue just receiving damage, then you don't think Saku took more VS Arona?
What about Fitch vs Gsp...lost every round but still kept fighting...man is a machine
Echoing the Diaz-Penn sentiment, Penn showed a ton of heart sticking in there against Rory as well.
I agree with that for sure.
TTT
nick diaz nut hugger -RileyPust - Echoing the Diaz-Penn sentiment, Penn showed a ton of heart sticking in there against Rory as well.
I almost made a mention of that in the post, and I should have, honestly. I think in that fight the difference was that Rory stepped off the gas pedal a little bit in the third round, something Diaz didn't do. Both were pretty bad beatings in which Penn showed tons of heart, I just think the fight with diaz was a little worse because Diaz never stopped applying pressure.
I mentioned those fights BTW NDNH on the last page bro. I figured you'd like this thread man.
Matt Brown vs. Pete Sell comes to mind.
Probably not "most courageous" ever, but Maia vs. Silva and Hardy vs. GSP, as both guys were seriously outclassed but never gave up.
I know Mayhem isn't too popular around here anymore, but his fight vs GSP was crazy, I've never seen someone smile so much while getting their ass completely handed to them.
Herring In A Fur Coat -
JDS-Cain 2 comes to mind
Lost to much $$$ to give any credit in that one Herring! He back straight TF up, unfuckin real bro!