Japanese professional wrestling does this in a number of ways. Most Japanese wrestlers start out as lower-than-dirt Jobbers who lose pathetically unless they're wrestling each other, in which case they use stock moves to decide the victor (the German Suplex is a huge crowd-pleaser in Japan partly because it is the official finisher of anyone who doesn't have a distinct finisher yet). After spending a few years as total losers, these wrestlers will then get Put on a Bus to wrestle overseas, after which they come back with a more distinctive wrestling style and a new, more badass Finishing Move that allows them to climb the ranks. This gets taken even further in some promotions, in which the new finisher becomes So Last Season and the wrestler breaks through to the very top with another finisher and another level in Badass.
One of the most famous uses of this was the All Japan Pro Wrestling 1995 Champion's Carnival. Akira Taue had spent years as a bit of a Creator's Pet because, while a competent grappler, he was constantly Overshadowed by Awesome in his tag team with Toshiaki Kawada and was given top billing despite being nowhere near the level of fantastic main-event technicians like Mitsuharu Misawa, Kenta Kobashi, Steve Williams, and the aforementioned Kawada. However, during the Carnival (a round-robin tournament for a title opportunity), Taue discarded his goofy agility-based offense in favor of brutal power moves that better suited his height and awkward build. The more power-based moveset and accompanying winning streak made a Dark Horse Victory look very plausible going into a match with the nigh-unbeatable Misawa.
One somewhat related example is Kazushi Sakuraba, who wasn't anything remarkable as a pro wrestler, but then switched to real-life fighting and became one of the greatest mixed martial artists of all time.
This is often the result of a push after a wrestler turns heel or face. One example would be the late great Owen Hart. Although always a talented wrestler, early in his WWE career he had a fairly plain gimmick and was often booked to lose. After he turned on his brother Bret Hart, he was given the win in their classic Wrestlemania match and became a credible threat to anyone on the roster.
Likewise, Lita was already tough as a valet then leveled up when she began taking on men, and again in a lost baby angle with Trish where she reached levels of brutality you usually don't expect from the male competitors.
Steve Austin started his WWF career as just a random henchman of Ted DiBiase, but thanks to a now-legendary promo at the 1996 King of the Ring event ("Austin 3:16 says I just whooped your ass!"), Austin gradually transformed into the stone-cold bad ass that fans eventually grew to love, cementing his place as a true legend of the ring and helping to put pro wrestling on the map in the late 90s.
The Rock started his career as a talented yet under-appreciated face, but after he turned heel, he began his rise as the "most electrifying man in sports entertainment".
Jimmy Jacobs, in IWA Mid-South and Ring of Honor. He came into both promotions as a jobber but was forced to become tougher during a long running feud with Alex Shelley that saw him get promoted to the heavyweight division despite being anything but in IWA while in ROH it was his refusal to give up in a feud with BJ Whitmer, as a side effect of trying to win Lacey's love.
Santino Marella has arguably taken one of the more natural evolutions into this trope, starting off as an incompetent jobber that often served as the punching bag for the majority of the roster, Marella has slowly shown more impressive agility and actual wrestling skills and become Tag Team Champion alongside Vladmir Kozlov. While still played for comic relief, at least he can actually pull off the Cobra now.
Santino started as an inversion of this trope, actually. His first appearance (in WWE anyway) was being called out as a "random fan" during an event in Italy, where he ended up not only fighting Umaga for his Intercontinental title, but BEATING him to claim the championship. For a while he was portrayed as a somewhat talented if amateurish technical wrestler with a couple of unique mannerisms (usually odd mispronunciations or choice of words), who slowly lost level after level and devolved into a complete Cloudcuckoolander. He finally seems to be getting a bit better, bringing him into this trope again.
He's still a bit nutty (The Cobra, anyone?), but as of the 2/17/12 Smackdown, he somehow survived a battle royal, being one of the last four out of twenty superstars, and took out Ezekiel Jackson, Drew McIntyre, and David Otunga for this prize: to become the last wrestler for the Smackdown Elimination Chamber. The only thing that remains to be seen is how he'll perform.
He was one of the last two in the Chamber match (and eliminated two competitors), put the Cobra on Daniel freakin' Bryan, and seems to be getting huge pops from the crowd. There seems to be a potential push here, and his goofiness only seems to help give him a hint of Crazy Awesome.
As of 3/5/12 he's taken enough levels to actually defeat Jack Swagger and become the new United States Champion.
The Miz started off as an annoying goofball who could barely remember lines as the host for the Diva Search. Now he's WWE Champion, and holds his own pretty well against such established stars as Randy Orton and John Cena.
Miz even defeated Cena at WrestleMania during the main event to retain his titlenote Yeah, The Rock sorta helped by attacking Cena beforehand, but still.... It didn't stick, but hot damn, it's still pretty impressive for a guy who started off doing reality shows.
Mark Henry arrived in WWE in 1996 and was immediately billed as the World's Strongest Man and given a push. However, due to injuries and a number of embarrassing gimmicks, he was always treated as an afterthought by wrestling fans despite his size and strength until 2011 (15 years later), when he pulled a Face–Heel Turn and was booked hard as an unstoppable monster. He eventually won the World Heavyweight Championship by absolutely destroyingRandy Orton, and has been demolishing everything in his path ever since.
Many WWE Divas came into wrestling from other venues, such as gymnastics, dance, or even modeling. However, they do train hard and inevitably improve, and gradually the quality of their matches goes from "Ugh, that was terrible" to "She's not too bad against a good opponent" to "That was slightly better than a carry job should be" to "Wow, she's gotten really good, where did that come from?" Michelle McCool, Layla and Eve Torres have all done this in recent years.
Madison Eagles started off in SHIMMER has half of a jobber Tag Team even usually neutral journalists claimed weren't worth bringing in to a dominant two time champion who Pro Wrestling Illustrated called the best in the world.
Candice Michelle in 2007. She won the Women's Championship and was voted "Most Improved Wrestler of the Year" by Pro Wrestling Illustrated and is currently the only woman to have won that prize.
Ice Ribbon as a promotion. It started off with a bunch of teenage rookies on mats in place of an actual ring, and ended up not only with a squared circle or two to its name but one of the first world wide internet streaming programs in 19 Pro and the physical ability to tour through multiple countries in Asia.
Once upon a time, there were two brothers: Brett and Brian Major. They were a tag team, standard fare...and then they teamed up with Edge and became Curt Hawkins and Zack Ryder. Then they became part of La Familia, then split up, and one went to ECW. Here we focus on Zack Ryder, who wasn't billed as 'great' to begin with. Hailing from Long Island, dressing himself as if he was a wrestler in the Attitude Era, he still didn't make it. Then he created a web show in a last-ditch attempt to get noticed and not get fired. After struggling to make a name for himself on the web, garnering support from fans and other wrestlers alike, and polishing his in-ring technique to no end, he eventually got a Number One Contender's match at WWE TLC 2011 and became the new United States Champion. WOO WOO WOO. You know it.
Sheamus was known to be a powerful wrestler when he debuted, but then got pushed out of the spotlight for quite some time. Cue late 2011 and here he comes, being the only person to stand up against a monstrous Mark Henry, and was powerful enough to kick the World's Strongest Man unconscious. Also, he was able to get out of the Khali Vicegrip by pushing it off with his own hands. It seems that Sheamus is going back to being the badass he originally was.
Not to mention the youngest Tokyo Sports MVP and G1 Climax champion ever.
While Daniel Bryan is certainly no slouch as a wrestler, he experienced a textbook case of this trope in the summer of 2013, wherein he was determined to prove that he wasn't the "weak link". This would lead to absolutely badass moments, including, taking out The Shield by himself during one episode of SmackDown, defeating Randy Orton cleanly on Raw (or as cleanly as a win can get in a Street Fight), and ultimately pinning John Cena cleanly at SummerSlam. To put it in perspective: That pinfall loss was the first time since losing to The Rock at WrestleMania 28 that Cena ever lost without any outside influences.
Prior to summer 2013, Windham Rotunda aka Bray Wyatt was best known for an unimpressive stint in the Nexus as Husky Harris where he was quickly sent back to developmental. Two years later, Rotunda returned under the Bray Wyatt gimmick and immediately made an impression with his dark and downright disturbing promos that demonstrated his incredible mic skills. While his initial match with Kane at Summerslam '13 was mediocre, Wyatt quickly improved, and in the following months proceeded to beat Daniel Bryan clean at the Royal Rumble and then pit his stable against the Shield in a match of the year candidate at Elimination Chamber. Not bad for someone who was once best known as "that fat guy from the Nexus".
The Shield themselves started out as a standard Dirty Coward hive, being formidable as a unit, but usually useless against equal numbers or even just anything short of a three-on-one assault. As time passed, they developed into a formidable Wild Card team, with aforementioned rivalries against the The Wyatt Family and Evolution. This only continued as the team split up, making them worthy individual opponents who vied and sometimes succeeded for title shots (yeah, Seth Rollins fights dirty, but he can still often look impressive and cunning about it at least).
Jax Dane's time in the National Wrestling Alliance has been a drawn out example that looks pretty straight forward in hindsight. Houston Heavyweight Champion, unifies with the Texas Heavy Title to become Lone Star Heavyweight Champion, then becomes National Heavyweight Champion, then North American Heavyweight Champion, then becomes World Heavyweight Champion. Also, his time teaming with Rob Conway under Bruce Tharpe is simultaneously Badass Decay and Took a Level in Badass for the NWA as a whole. While NJPW used to be an NWA member who had a say but ultimately answered to its authority, the angle had the NWA at the same level as NJPW's many power stables such as Suzuki-gun, CHAOS and Bullet Club. On the other hand, it was the first time in years NWA was seriously on the Japanese national stage since maybePro Wrestling Zero 1's short peak.