Done in The Order of the Stick, where Elan takes a level in badass — or, rather, in the Dashing Swordsman prestige class.
Vaarsuvius also does this (albeit only temporarily through a Deal with the Devil) in order to save [his|her] children from a really pissed off dragon.
And in a less literal sense, Elan has also become somewhat less incompetent at using his regular Bard abilities over time.
Roy took a level too. In the beginning, he was just a snarky team leader. The only time he showed his inner awesome was rescuing Elan from a situation he wouldn't have been in if he hadn't abandoned him in the first place (and him taking down Xykon, but that was via deus ex machina). After his little trip to heaven, he suddenly becomes more serious, has a worldly air around him, beats on a half-dragon-half-ogre, most of a bar in a barfight, gets ranked top of the list after beating Belkar (whose awesome used to be far above him) and bopped Haley's uncle across the room. Aside from asking Belkar to find him a cartographer ("...this is a cart of gophers, isn't it?"), after being resurrected Roy has not made one bad descision or done anything that has come back to bite him.
Belkar, but more like regained his level of badass. He comes down with a curse caused by his mark of justice. Then when the curse is broken, this happens. Complete with a kiss at the end!
Redcloak took a literal level in badass in this strip and the two following, showing off his newfound powers by soloing the entire Resistance and leveling its base.
In a more plot important example, Dave, the nerdy, chain-smoking everyman grows more and more badass over the course of the series, finally ending in his becoming the most powerful Mad Scientist in the series, curb-stomping Helen, Mell, and Madblood with ease and coming pretty close to destroying the world.
Torg of Sluggy Freelance has always been a goofy Cloud Cuckoo Lander, but with the comic taking on more serious themes in addition to the goofy ones, he's had to cope with more and more dramatic and dangerous situations. The real shift happens in "That Which Redeems", a story during which he's stuck for months on an alternative Earth fighting against invading demons — he both learns how to fight for real and finds out that the fancy sword he'd picked up during time travel to the past is magical and can be Powered by a Forsaken Child to become powerful enough to cut like a lightsaber and literally kill a god. After that, he remains goofy, but is quite capable of getting dangerous when needed.
Riff: "Dude! When did you learn to kick ass?"
Torg: "I've been taking an internet college correspondence course in kickass."
Riff: "You have not."
Torg: "But I so want to teach one!"
Agatha takes several levels of badass in Girl Genius as she evolves from from the hopeless klutz of Polygnostic University to a Spark at or above the level of any previous Heterodyne.
Gil's evolution from a bored pupil constantly tested by his father for basic worth into a man capable of facing down his father, and an army of war clanks, is a clear example. See here for evidence.
More recently, Boris, the Baron's personal secretary, has suddenly shown his ability to not only take down a Jaegermonster, but actually beat him until he gives up classified information. This is actually a classic example, in that there was no on-screen intermediate development.
Mentioned again. This is either a single continuity nod to the fans who insisted it was real, or will become the most epic 3rd line ever.
The character Cale'Anon from the webcomic Looking for Group. He starts the series off rather clueless and useless, and in the first comic gets blasted to cinders by Richard. By the third or fourth issue, he's changed a little and very soon is pulling stunts like this and this .
For some of the more unconventional crossovers in the Hellsing fancomic And Shine Heaven Now, the characters from that crossover have done this. The prime example is Madeline from the books of the same name: a sweet schoolgirl in the books, a regenerating vampire hunter in Shine.
The Parcel Mistress starts out as just a simple mailwoman who wouldn't hurt a fly. By the end of Act 5 she's a space-warping One-Man Army on a Roaring Rampage of Revenge, and one of the most powerful characters in the comic.
And then there's Jade, who was a competent, if underpowered latecomer to the game, and her Alternate SelfJadesprite — a depressed, completely ineffectual fussbudget. By the [o] intermission, Jade is easily holding her own against the Big Bad, partially because the spirit of her dead dog and surrogate parent won't let him fight her, and Jadesprite is in control of her emotions enough to deliver a tactically-critical piece of hardware to another character. In [S] Cascade, Jade and Jadesprite ended up merging into a combination of a God TierWitch of Space, a First Guardian, and a Sprite — making her the most powerful heroic character and second only to Lord English in absolute power.
Here's an easy rule to remember: is this Homestuck character a badass? If no, they will be. If yes, they will become even more of a badass. Dave is another great example - at the beginning, he's thoroughly Cherry Tapped by Bro (who, admittedly, is a pretty amazing badass in his own right). A little later, he denies that he's a hero, guessing that he'll become a hero when he becomes 'future Dave'. By Cascade, he has already aided the other three kinds in innumerable ways, and in that flash he takes the final step to becoming God Tier.
And Aradia: she was already pretty powerful, but her ascent to God Tier made her powerful enough to stop Bec Noir in time.
Criminy of Sin Fest has grown a massive pair in about a week's time. Went from meek nerd to telling the resident Jerk AssHolier Than ThouKnight Templar Seymore off, digging his way into the maw of hell for Fuschia, then holding his own in a fight with a demonic pitch fork. Awesome.
Dubious Company handled this very subtly. At first, they have trouble fighting anything other than Kreedor's rookies. Later, the pirates attack Mary and Sue, AKA: The Sues in their sleep and still need to fight dirty and outnumber them. Then during the rematch at Kreedor's castle, the pirates are barely holding their own going one-on-one. Later still, The Sues, Stus, and Tiren team up against a dragon. The pirates' Tiren holds out the longest.
Katherine Gilchrist, the spooky-eyed, introverted, generally strange fabrics expert at the museum where protagonist Monica Villareal works in Wapsi Square has leveled up after her Mesa Verde adventure, to the point where she seems to be perfectly willing to scream at The Library, which has the power to jerk Titans around.
Dragon Ball Multiverse: And how. A ton of characters in various universes have improved in both skill and power over their U18 counterparts. To form a list:
U3 Bardock, who keeps the future sight, has gone Super Saiyan, and has become older and wiser, and even took the Saiyan throne from Vegeta.
U4 Zen Buu, basically a Super Buu who managed to absorb everyone with a power in his universe.
U6's Bojack Gang, who actually defeated the Z-Fighters. And, without said Z-Fighters to stop him in his inevitable second coming, they may have actually defeated Broly as well, though the fact that Broly hasn't slaughtered them may simply be a plot-hole.
U7's Gast Carcolh... Who is basically the entire Namekian race fused with Nail, who defeated Freeza, Cell and Majin Buu in his universe.
U8's King Cold. In U18, he begged for his life like a coward when Trunks turned up. This time, despite knowing that he's outmatched by many fighters, he goes up to his true form anyway, which, had U18's version used in his fight with Trunks, would've allowed him to defeat him and Goku.
Nearly everyone in U9. Yamcha is an android, Tien easily defeats Sun Wukong, and Videl not only has the Z-Sword, she can use the Kaio-Ken and actually give King Cold a good fight in his intermediate form.
U10 shows off what Nail would be capable of had he actually helped fight the Ginyu Force on Namek - let's put this into perspective, this Nail could've defeated Recoome, who Vegeta couldn't defeat back then. Yes, Nail has been listed twice, but he is pretty awesome.
Future Trunks, from U12, actually managed to give his U18 father (who is a Super Saiyan 2, just to note) a good fight, despite not being quite up to his level in power.
U13 Nappa and Raditz, the latter of whom has a technique allowing him to become an Oozaru at will without a full moon (fake or otherwise), and in such a form actually managed to put up quite a fight against the U3 version of his father. Same with Nappa, who, while he can't quite keep up with his Super Saiyan comrades either, manages tomock the hell out of Freeza.
U16 has a couple - Vegito was ridiculously powerful in U18, sure, but here we see the true extent of his power against Broly, and it is awe-inspiring. Bra, being his daughter, isn't the girly-girl like her U18 counterpart (which is lampshaded in a side-comic), and is ridiculously powerful in her own right, even if she does have some serious anger issues.
U17 Cell, who defeated Gohan in their final clash, and slaughtered the Z-Fighters easily, and likely went on to kill the Bojack Gang and Majin Buu as well. And, much like U6's Bojack Gang, may have actually managed to kill Broly when the latter arrived on Earth (or this could simply be a plot-hole as well).
Crest in Flipside, after being Demoted to Extra for nine real-world years, makes a comeback by roughing up the gang he was terrified of the last time he was a main character.