I don't think I've replied to this thread, but let me throw in my two cents with a few concrete reasons as to why. There are a lot of really "influential" figures in MMA, but I'm going to try to name a few that influenced MMA as a whole and not just what occurs in-ring.
1) Rorion Gracie - Rorion was the marketing and conceptual impetus behind the first 2 UFCs, back when it was known as NHB (No Holds Barred) fighting. His premise was simple, take the same thing that the Gracies had become infamous for in Brazil, and present it to a world-wide audience. Well, 14 years and 70 events later we find ourselves entrenched within a new rennaisance in combat sports and Martial Arts in general.
2) Royce Gracie - If you were picking through the line-up of competitors for a winner in the initial UFC, you probably would not have given the young 180lbs grappler in a gi a chance. However, through artful technique and dogged persistance, Royce became an icon after the event and help revolutionize everyone's general perception of fighting. As a result, Brazillian Jiu-Jitsu (and submission skills in general) is a staple component that needs to be in each MMA competitor's tool box.
3) "Big" John McCarthy - This large speciman of humanity has been a UFC mainstay since the second UFC event back in 1994. Not only is he the most recognizable face in MMA refereeing, but he is the defining bar of officiation when it comes to MMA. Not only the best in the business, but Big John was there from the beginning when the unified/NJ rules were put into place. If anyone has questions on the rules, Big John is your definitive source--he helped write the book!
4) Ken "The World's Most Dangerous Man" Shamrock - Now this may vex some as to why I place him here on this list. Ken has had a long, storied career that spans the long gone glory days of Pancrase Hybrid Wrestling, to the UFC, to the WWF/WWE, back to the UFC and now in the IFL and has had less than stellar outings as of late. So why do I place him here? Simply put, Ken Shamrock is the defining archeatype for a marketable champion and is the UFC's first bona fide "super star." He had the look, the charisma, and an admirable set of skills and talent to back it up. There is a reason why CBS chose him to spotlight on the "World's Most Dangerous" list, and (like him or not) his personage has been a pioneering and driving force for MMA for a long time now.
5) Mark "The Hammer" Coleman - Mark Coleman was the driving force behind the amateur wrestler's presence in MMA. As a heavyweight, "The Hammer" was not only a domineering visage, but he was also dominant in his early career. He showed that a wrestler's ability to take down and ride an opponent out while punishing them was a valuable tool. While Ken Shamrock and Dan Severn had used "ground and pound" tactics in fights they had before, it was Coleman's vicious implementation of the style that gained its coined monicker. With Coleman's entrance into the UFC, he gave a lot of competitive grapplers an avenue to keep competing outside of the collegiate realm and it opened the doors for many an aspiring MMA competitor (Mark Kerr, Kevin Randleman, even Randy Couture - just to name a few).
6) Maurice Smith - "Big Mo" is to strikers what Mark Coleman is wrestlers. With 75 professional kickboxing matches spanning over 11 years (62W/45kos, 9L and 4D), his striking pedigree is probably the best in all of MMA to date. However, no one gave him a chance once he stepped into MMA to compete. Grapplers were all the rage and they were viewed as unbeatable monsters by the grand majority of NHB followers, and with good reason (Art Jimmerson, Milton Bowen, Ron Van Clief, and the list goes on). After his stunning TKO win over Conan Silviera, those with their ears to the ground began to take notice. After his win over Mark Coleman, people were wondering what had just happened. Maurice Smith had single-handedly put the striker back on the MMA landscape, showing that a fighter who is primarily a striker is dangerous when trained correctly and confidently opened the doors for other strikers like Chuck Liddell, Mirko Fillipovic, Mark Hunt amongst many others.
7) Frank Shamrock - This man needs no added nickname. Love him or hate him, you cannot deny his presence in the MMA ring. What made Frank Shamrock such a force? Was it his grappling skill? Was it his striking skills? Was it his unparalleled conditioning? Well, to be completely honest, it was all of those things. He wasn't an elite "master" in any single discipline. Rather, he was excellent at all of them. As a result, he was dangerous in all fight situations: Standing and striking, taking his opponent down and wrestling, fight off his back with submissions, and was strong from the beginning of the fight all the way into the later minutes. Frank Shamrock is the archaetype that defines what a modern MMA competitor needs to be, a jack-of-all-trades that is competant (and dangerous) in all fighting situations.
8) Kazushi Sakuraba - If you bring up Sakuraba's name to many newer fans, you may be met with ambivalence. However, you bring up Sakuraba's name to MMA competitors and you will be met with never ending praise and respect. It isn't just because he's a nice guy. Rather, Sakuraba is one of the fiercest and most cerebral of competitors that has ever stepped into MMA. When the Gracies were completely untouchable, Sakuraba proved that the "riddle of BJJ" could be solved and not only beat them, but he did so in dominant fashion. But his accomplishments were not confined to simply being "The Gracie Hunter," as he faced a wide variety of opponents (many of which were much larger than him) and brought something new to the table each and every time. A large number of techniques were considered completely ridiculous within the MMA realm before Sakuraba showed that it could be done and utilized regularly and lethally (turning side kicks, jumping stomps and punches, the cartwheel guard pass, the mongolian chop, amongst many others). Further, his showmanship was apparent inside and outside of the ring, which proved that fighters could be more than just voiceless machines (Sudo, "Mayhem" Miller, "Rampage" and many others can thank him for that). Above all else, Sakuraba proved that tons of heart and a quick mind were indispensible to the modern MMAist.
9) Randy Couture - Randy is very unique on this list as he has been present through both the "Old" and "New" UFCs, and has been highly competitive and successful while doing so. While his W15/8L record isn't stellar in mathematical terms, the accomplishments he has garnered while building that record are phenomenal. He is the first 5-time UFC World Champion, and the only UFC champion to win belts in multiple weight classes. He has done all this while competing with athletes a decade or more younger than himself which is unheard of in combat sports. Further, he continues to be one of the most modest and stellar ambassadors for the sport of MMA. Above all else, Randy has proven time and again that the modern MMA competitor has to train dilligently and must be able to change his gameplan for each and every opponent to be successful. While many MMA competitors fall into routine fight plans and depend on a select set of tools fight-in and fight-out, Randy has proven over and over that you have to continuously learn and expand your game to stay competitive. That is the biggest reason why Fedor is a stalwart Couture fan.
10) Dana White - Whether you love him or hate him, you have to respect Dana White. As a reformed boxing promoter, Dana had a vision for the UFC (and MMA in general) that eclipsed the simple promotion of a martial arts style. When Dana White re-launched the UFC under the Auspices of Zuffa, he did it with hopes to legitimize MMA as a sport. Fast forward 41 events and 6 years later, the UFC is now one the hottest items on PPV, has a weekly cable show, is holding international events, and is now being embraced by ESPN and Sports Illustrated. Now, everyone knows that the Fertitas front the money, but the planning, marketing, and management efforts have been handled (for the most part) by Mr. White. Love him or hate him, MMA would not be where it is if he was not part of it.
Now there are many others out there that can definitely be mentioned, but doing so will make this already long post even longer. That's my list (for now). I hope it didn't bore you.
It doesn't matter if you agree or disagree
... As long as I don't bore you and I spark a moment of thought, my goal is achieved
Queng leon queng tigre ecu tacacut, queca pa? - Pampangan Mandarigma Motto