Usagi from Sailor Moon might be one of these. She starts out as an ordinary school girl, then quickly gains magical powers, a small platoon of new friends, a destined love from a previous life, and finds out that she's a princess who's going to rule the world sometime in the distant future. Though considering Usagi's personality, that last one might not be so great after all.
Haruhi Suzumiya. Somewhat deconstructed, especially considering she's the closest thing that the early novels and the anime have to an antagonist...
One could argue that Kyon is more of an escapist character. He's reportedly very smart (though he never claims it), constantly making witty comments, and is surrounded by three female characters, one that's likely to appeal to you.
The other Haruhi from Ouran High School Host Club. A poor girl with incredible grades, great cook, and surrounded by six drop-dead gorgeous men (and making snarky comments all the while)? Yep, Haruhi definitely fits here.
Golgo 13. The thing about Mr. Togo is that, yes, he's a nigh-unstoppable assassin with aim such that he's unironically referred to as the Hand of God, with more money than the entire nation of Japan, who regularly talks women he's never met before into bed... but he doesn't seem to enjoy any of it. Verges on deconstructing the idea.
Alucard from Hellsing. Seras is also an example, as she goes from a police girl with a tragic past to an elite vampire soldier and even takes Alucard's position for a while.
It could be argued that there are Escapist Character tendencies for most of the cast. There are many scenes that may and probably will go beyond suspension of disbelief, but the stylization with which Hirano pulls it off is so awesome that it can be excused on account of Rule of Cool.
Love Hina's Keitaro Urashima. For everyone who ever couldn't get a date, what could be better than suddenly becoming the guy in charge of an all-girls inn, with an onsen, where practically all of them eventually fall for you? Sure, there's the physical pain inflicted on a nearly daily basis, but most would agree that it's Worth It.
Of course, this also pretty much applies to the protagonist in any harem series. Tenchi Muyo!, Maison Ikkoku, etcetera. Amusingly, one of the biggest complaints about these sorts of characters being wishy-washy ignores the fact that it's the easiest way to make an escapist character not feel openly exploitative of the situation.
Thirteen Dot Cartoons was incredibly popular in Hong Kong in the '60s and '70s, but mainly among a much lower economic class than its protagonist, who could never afford the fancy clothes she wears or all the things she buys. Plus, since she's a dimwit, readers got to feel good about themselves even as they wished they were someone else. Notably, after the recent growth of Hong Kong's economy there no longer seems to be as much of a market for the series.
Yami Yugi from Yu-Gi-Oh!! I mean, what Shrinking Violet hasn't wanted, at least once, to beat up the school bully and get away with it?
Guts from Berserk can be seen as this. Even though some really nasty and horrific things do happen to him the whole time, his conviction in facing opponents that would terrify a normal human being, along with his cool sword and great look, probably make him someone to admire.
Ciel of Black Butler. An incredibly rich and beautiful Teen Genius that nearly everyone loves and respects who has an almighty BishounenBattle Butler that can grant his every wish and can be extremelyclose to him at times? Not to mention his Dark and Troubled Past (which he was 'rescued from' by the aforementioned butler), Even the Guys Want Him, he works for the queen, and he owns the largest toy company in Britain...all starting before the age of twelve.
Simon the Digger of Tengen Toppa Gurren Lagann. His beloved adoptive brother is Kamina, he hangs out with Yoko and Nia, almost everyone around him is incredibly supportive and he ends up leading a rebellion against (in order) an earth-wide tyranny, then a universe-wide tyranny at the ages of about fourteen and then about twenty-one. In a world where mechs quite frequently do the impossible, he's literally the best Gunmen pilot there is.
Superman. The name "Metropolis" comes from the Greek and Latin roots for "city," so Clark Kent is basically Everyman, Everywhere.
More specifically, he was the 'Man of Tomorrow ', i.e. he was supposed to be what ordinary people might dream of someday becoming.
Batman. Grant Morrison actually talked about this and claims that for all the talk about how much of a fantasy Superman is, Batman is even more so:
"Batman is obviously much cooler, but that’s because he’s a very energetic and adolescent fantasy character: a handsome billionaire playboy in black leather with a butler at his beck and call, better cars and gadgetry than James Bond, a horde of fetishfemme fatales baying around his heels and no boss. That guy's Superman day and night. Superman grew up baling hay on a farm. He goes to work, for a boss, in an office. He pines after a hard–working gal. Only when he tears off his shirt does that heroic, ideal inner self come to life. That's actually a much more adult fantasy than the one Batman’s peddling but it also makes Superman a little harder to sell. He's much more of a working class superhero, which is why we ended the whole book with the image of a laboring Superman."
Or as a comedian put it: "I wish I was Batman; not so much the fighting crime, I just wish I was rich and my parents were dead."
Captain Marvel took up the Wish Fulfillment a notch by taking Billy Batson, a boy within the age range of the target demographic, and giving him the ability to transform into a superhero very much like the one kids were into at the time. Unfortunately, the courts agreed with DC that it was a little too similar (which interestingly ended up with them in the same universe).
Kitty Pryde of the X-Men is this trope personified. Started out as the team's Naïve Newcomer, and grew up to be a Badassninjagenius with a petspacedragon and Gentle Giant boyfriend. And the fandom rejoiced, for they watched every step of this journey from Everygirl to Super-Special Heroine and wished they could be her (or "be with her").
In the case of both Storm and Wolverine, sometimes this got carried so far that even for teenage dreamers, it became something of a running joke. For example, the infamous scene where a depowered Ororo somehow manages to defeat Scott Summers in a Danger Room contest, using rules which he more-or-less could not lose under. She manages to dodge energy blasts moving at the speed of light, more-or-less, and it was so blatant that even many of the fanboys ended up saying 'what?' And Wolverine, after a while, simply became a running joke with a Lampshade on his head much of the time.
Spider-Man straddles the line between This Loser Is You and an Escapist Character pretty much constantly. No matter how much his life ends up sucking (Hero with Bad Publicity, dead parents and uncle, "rocky" love-life pre-MJ, One More Day) he's a superhero who gets to web-sling from skyscrapers and he always has a quip ready. There's also something very appealing about an everyman amongst so many other powerful superheroes (even more so when you consider how most Marvel Universe characters are everymen already).
Aladdin. In just 90 minutes he went from living off stolen food to having the friendship of an all-powerful-genie-Robin-Williams, a flying carpet, the affection of the richest, most desirable girl in the kingdom, and an assured future as the next Sultan — and this status remains through two movies and 86 half-hours. That's pretty darn escapist.
For a meta in-universe example of this trope, there's a wild theory that Ferris himself is an Escapist Character created in Cameron's mind (kind of like Fight Club), so he could manifest his wish to break free from the boring routine and face his social fears (and specially his father).
Limitless presents us the answer to “What if they make a pill that would give you Super Intelligence?” Eddie Morra takes Wall Street by storm and wins millions by only taking a pill. Sounds like fun? But if you get everything you want by only taking a pill, you felt entitled to a lot of more other things without any effort. The movie deconstructs Eddie into a Jerkass with Acquired Situational Narcissism that cannot recognize where is the Moral Event Horizon anymore.
Smith from Shoot 'Em Up is a master of every firearm known to man, kills dozens of people in increasingly more creative ways, battles strawmen on both sides of the political spectrum, gets to have sex with Monica Bellucci, and rams inconsiderate drivers off the road without consequence.
Word of God states that the Avatars Navi were designed to be a whole race of these.
Sherlock Holmes can solve any case, no matter how bizarre, and can identify a person by a strand of hair inside a hat! And right so inhumanly often. (People tend to forget the cocaine addiction and original shut-in nature.)
Harry Potter, before the Cerebus Syndrome set in. His character is almost entirely this in the first book (an abusedorphan discovers that he is rich, famous, and oh yes, a wizard), but the following six consist of him slowing learning just how much It Sucks to Be the Chosen One.
Bobby Pendragon in the Pendragon books starts out this way. That is, until we see just how awesome a villain Saint Dane is. And maybe even after that too.
Bella Swan (for Twilight's target audience). Her oft-complained about blandness was not a result of bad writing, but a deliberate decision on Stephenie Meyer's part so readers can step into her shoes more easily and experience what it's like to be loved by Edward Cullen.
Lord Peter Wimsey has elements of this: Dorothy L. Sayers created the character when she was desperately poor and got a certain satisfaction from making him the richest and most self-indulgent man in London.
Artemis Fowl. Doesn't have to go to school because his parents are either missing or bedridden. He has a Battle Butler and enough money to indulge a self-admitted childish belief in fairies and magic. Though only 12, he's treated like an adult.
Percy Jackson. So what if you don't do well in school, and your stepfather is a jerk? You're really a super-powerful demigod with Poseidon for a father, and you get to do cool stuff from now on!
Dagny Taggart of Atlas Shrugged. Whilst she is clearly an idealized author avatar, a significant portion of the book's female audience has found Dagny provides a satisfying fantasy for them, as well. Of course, like most things relating to Atlas Shrugged, Your Mileage May Vary.
Tyler Durden of Fight Club basically exists to pass on Testosterone Poisoning to the men of The Nineties. This was subtly parodied in the book, but lampshaded like a mofo in the movie.
Tyler Durden: I look like you wanna look, I fuck like you wanna fuck, I am smart, capable, and most importantly, I am free in all the ways that you are not.
Honor Harrington, at the latest point in her series, is a starship commander, the most victorious admiral in her either of her two nations' histories, the first or second highest ranking officer in both militaries, a feudal lord in both those nations, filthy rich from prize money and her landholdings, is genetically engineered to be stronger and faster than the average human, has several bionic implants, is one of the few humans to be mentally bonded with a friendly but badass alien companion, and Married both to a handsome, intelligent man and his kind and loving wife. To top it all off, every one of her victories, titles and ranks was earned by her own hard work and talent. If only all of our toils paid off as well as hers!
Data from Star Trek: The Next Generation and Spock from Star Trek: The Original Series both serve as the same sort of wish fulfillment archetype for socially awkward Trekkies. To wit, they're smart, respected, physically powerful, long-lived, and they're blessed with loving and devoted friends even though they themselves have never learned human social skills.
Riker. Has a killer beard, grew up in Alaska, knows martial arts, plays trombone, will wipe the floor with you at poker, isn't afraid to break the rules, unflappable (well mostly)... And then he turns out to be an augment exile in one of the books. Squee!
Kirk. Spock is smarter than him and probably stronger than him, but Kirk gets a spaceship. And women. Don't forget the women.
Wesley was intended to be this to young viewers; a kid who could hold his own and had skills gradually prove himself to the crew as someone useful.
Worf also became this in many of the more Klingon-centric episodes. The Proud Warrior Race Guy is usually pretty popular with the Fanboys.
The Doctor, from Doctor Who. Owner of an effectively self-powering, Bigger on the Inside time machine that lets him go anywhere in time and space he feels like - and no matter where that is, his ability to save the day lets him get away with acting (and dressing) like a complete lunatic regardless of cultural norms. Oh, and his travelling companions tend to be attractive twenty-something women.
As a corollary, the Doctor's companions (especially Rose, who was explicitly created for this). Many, many children in the UK have grown up wishing the Doctor would come and whisk them away to adventures in his TARDIS.
Jane By Design's Jane is shaping up to be this. She has multiple potential love interests, a fantastic job that comes easily to her, and all problems she has are quickly resolved.
Dr. House, despite the chronic leg pain and occasional mental breakdown, is really fun to watch because he skewers stupid people without mercy. And he pretty much always gets away with it. Who doesn't want to be able to tell coworkers and customers exactly what you think of them?
Back in the 70s, the Six Million Dollar Man embodied this in some ways (though Steve did have some problems his bionics could not solve). Interestingly, the other in-universe characters provided some counterpoint, there was another bionic man who had turned out to be psychologically unable to handle it, and Steve's lady-love Jaime Sommmers had recurring problems of bionic rejection that made her superpowers something of a double-edged blessing.
Breaking Bad's Walter White is an interesting example. He's a lower-middle-class teacher who gets crapped on in every possible way, including getting cancer... and he's also a meth dealer who is completely bad-ass. A lot of people can identify with the crapped-on part—in that sense, he's a This Loser Is You character. And then we fantasize about kicking ass, like Walt's alter-ego does. Like Harry Potter, just grittier. Much grittier.
You know those people who take too long at lines, are massive hypocrites, abuse animals, borrow money without returning it, or just generally piss you off every day? Do you wish you could beat up those annoying people with no consequences? Everett True can.
This is sometimes used to explain the allure of the Zombie Apocalypse. Yes, it'd be nice to finally pillage and burn to your heart's content without fear of reprimand, but even more promising is an environment rich in human-like targets where it's accepted — nay, encouraged — to unleash your inner sadist on anything that gets within ten feet of you.
Alex Mercer in Prototype. Why? Shapeshifting with no squick, easy Instant Expert, and by the end of the game is a God Mode Sue. However, everyone has wanted to be able to pick up a taxi and run down the sidewalk killing hundreds and that's just something you can do at the beginning. This game is the only stress relief you'll ever need.
Batman himself in Batman: Arkham Asylum. Something is just so fun about terrorizing the inmates that it doesn't matter that, as normal, Batman is Crazy-Prepared.
When one terrified opponent asks "What ARE you?", the urge to reply (out loud) "I'm Batman" is almost irresistible.
Fate/stay night's Emiya Shirou is a strange example. On one hand, he's so badass that even when he dies, it's a Crowning Moment of Awesome. He lives in a mansion, is capable of supporting himself without parents, and practically has a busty and adoring live-in girlfriend who wouldn't hesitate to sleep with him if he'd only notice. On the other hand, he's a textbook Broken Ace with literally no regard for his own well-being.
If you ever play either Modern Warfare game without imagining yourself with Soap's mohawk and Scottish accent, it's safe to say you've entirely missed the point.
Solid Snake from Metal Gear Solid is a subversion. The game starts by setting him up as an absolutely archetypal action hero (particularly the 80s action, KurtRussell type), a classic Escapist Character. As the plot progresses, the player learns exactly how miserable and shattered Snake really is. Unfortunately, some players missed the point; Kojima decided to be a touch less subtle in Metal Gear Solid 2 and gave us Raiden (an extremely vicious aversion of the trope) instead.
Kay Faraday from Ace Attorney Investigations is any fangirl (or boy)'s wet dream. She's a perky, smart thief who gets to tag along with Ensemble Darkhorse Edgeworth, is Gumshoe's bestest friend ever, most everyone is at least nice to her (even Jerk with a Heart of Gold Lang), and she even has a tragic past matching Edgeworth's so they have even more in common.
Apparently, Tim Schafer designed Raz from Psychonauts to be this. This is why he's human; originally, the game was going to be about a psychic ostrich. Seriously.
Not to mention Eddie Riggs, from the same creator: Riggs is a jaded roadie who feels his love for classic overdriven guitar riffs is underappreciated in an era of nu-metal emo teenage crap. He ends up in a world where his roadie skills allow him to create war machines and his guitar can make the emo kids' heads explode. This dude embodies every metalhead's secret fantasy.
Shepard, the Player Character from Mass Effect is the most Badass and important person in the galaxy, and the game lets you know it and experience it.
Sora from Kingdom Hearts got to live out millions of kids' childhood dreams of being involved in various Disney Movies. Add being the Chosen One into the mix and he's officially become the Escapist Character we all dreamed of being as kids.
Dante of Devil May Cry. A witty, snarky, BadassHalf-DemonHunter of His Own Kind who does all kinds of ridiculous over-the-top stylish stunts in both gameplay and cutscenes and runs his own kickass Demon Hunting business. Who wouldn't want to be as cool as him?
Sonic the Hedgehog. He's fast, powerful, and incredibly acrobatic. Who wouldn't want to be him? Shadow counts too.
Asura from Asura's Wrath is definitely one of these. He's extremely powerful, and can punch out planet sized objects. He seems to subvert somewhat, in that when his Old Master Augus thinks the way an escapist character should; fighting, eating, Drinking, and sleeping with babes, Asura seems to not like it much, and is only focused on retrieving the daughter the 7 Deities took from him.
The title character of The Fancy Adventures of Jack Cannon Sure, he doesn't get all the chicks (at least not yet), but he can beat you down faster than you can say, "Look out! Jack Cannon's about to punch you with his kung-fu-like action!"
The Kids in Homestuck. You can't get along with your parents and your only close friends are online, SHIT IT'S ADVENTURE TIME. And then it all turns out horribly wrong. Have fun!
Kirk in The Gungan Council is based heavily off of theKirk, and generally flew around in a ship blowing up things and getting lots of tail. However, brutally averted due to having a terminal disease.