Part-Time Hero

"So now that you've saved the world, what do you want to do today?"

"Same thing we do every night, Pinky -- patch Windows Vista."

—Commenters on Wapsi Square

The Part-Time Hero wants to save the world, sure. He wants everyone to be happy and alive, but he also wants a normal life.

So she's going to balance fighting off those Demonic Invaders with cheerleading practice or her job or dating. They're going to have episodes, even entire arcs dedicated to resenting their double life. (Particularly their fighting evil side cutting into their "me time.") This is a very popular trope in Anime, especially for Magical Girls (who have to balance their duties as heroines against the joys of homework and getting up to go to school in the morning).

This often includes the Superhero with a Secret Identity, but not all of them. Spider Man is more of an example than Batman is. Includes all Wake Up, Go to School, Save the World series, of course.

Compare Punch Clock Villain. Contrast the Punch Clock Hero, who seems similar at first but is far less heroic when he is not, well, being a hero.

Examples of Part-Time Hero include:

Anime and Manga

Sailor Moon wants so badly to go back to being normal that at the end of the first season, she uses the power of her newly acquired MacGuffin to wipe everybody's memories that anything had ever happened, turning her entire team back to normal. (Unfortunately, the Sorting Algorithm of Evil applied, and she was soon forced to undo this.)
Magic Knight Rayearth: Ryuuzaki Umi, one of the heroines, spends a considerable amount of time throughout the first season of the show whining about how she's going to miss an important fencing tournament if they don't finish up and get home Right Now. And when they get back to earth, it's clear that only a couple of minutes (if that) have passed. The second trip (in Rayearth II) "took" a couple of days, but they still spent more time than that in Cephiro.
Bleach: Ichigo isn't too fond of being a shinigami. Notably, he generally prefers not to get actively involved, and it takes someone to be in danger right in front of him or for one of his friends to be under threat to drag him into the fray. Thankfully for the continuation of the series, something always seems to drag him out of the classroom and back into his Shinigami robes. His tune changes once he actually loses his powers, and can no longer help his friends.

Comic Books

Spider-Girl has real problems with this. Her Superhero career tends to completely screw her civilian life, especially her attention span in school.
Superman has been portrayed this way Depending on the Writer.
Spider-Man had this in the teenage and college days of his career. Most spin-offs and reboots have this as a focus point to the point where many people refer to it as the "Spiderman dilemma"

Film

Paul Kersey from Death Wish maintained his work as an architect up through and including Death Wish IV: The Crackdown. Unusually for a plain clothes adventurer of 1970s and 1980s film, Paul Kersey did in fact maintain a dual identity/alter ego, since the general public did not know that Paul Kersey acted as the vigilante and Kersey continued his work as an architect while acting as a vigilante. In fact, his nightly prowls to find muggers to slay caused him to miss calls from business associates, who civilly asked him about this situation.

Literature

Mercy Thompson: Mercy has to keep up her job as a car mechanic while fighting whatever supernatural horror is threatening her friends this time. You know things are serious when she asks her ex-boss to run the shop for a day.

Live Action TV

The three sisters in Charmed spend a lot of time complaining about their duties conflicting with their personal lives. Half of the time the villains have to walk up to their front door for them to even pay attention.
Chuck Bartowski of Chuck is constantly forced to renege on personal commitments because national security is at stake.
Sydney Bristow from Alias attempts this valiantly for the first few seasons. Ultimately, all her non-spy friends are either brought into the conspiracy or murdered, so she pretty much goes all-in for the remainder.
Claire Bennet from Heroes.

Tabletop Games

Common to the point of default in the Teen Champions subgenre book.

Web Comics

Bob in The Inexplicable Adventures of Bob is self-employed at his newsstand, and it's a good thing, considering how often he ends up missing work. His customer Mr. Bystander seems to exist mainly to berate him for this.

Web Original

Whateley Universe: All of the kids in Team Kimba, since they're at the Super-Hero School Whateley Academy in the webfiction 'verse, and they're not supposed to be getting into superhero fights since they're minors. And they have classes they're not supposed to cut.

Western Animation

Kim Possible almost subverts this at times, as pretty much everyone knows she's off "saving the world" when having to ditch cheer-leading.
Terry in Batman Beyond does resent the loss of his free time to fighting villains, and there's considerable friction between him and Bruce, who treats normal life as simply a cover for crime fighting, since he became the mask long ago and never took it off despite never physically putting it on for forty years.
Largely avoided on Wonder Pets. In one story, the Wonder Pets take time off to join the circus and in another, they take a vacation. In both stories, however, they actually end up saving an animal. Also, they are generally always ready, willing and able to save animals, though Ming-Ming can sometimes be grouchy.
Happy Tree Friends: Splendid. This is probably a good thing.

Real Life

Every Reserve and Militia group in the world, though they can be upgraded to full time heroes.
Volunteer firefighters and Emergency Medical Technicians.
Lifeguards can be this, summer at the beach earning money, rest of year back at school earning a degree.