Plain Jane

I sometimes wished to have rosy cheeks, a straight nose, and small cherry mouth; I desired to be tall, stately and finely developed in figure; I felt it a misfortune that I was so little, so pale, and had features so irregular and so marked.

—Jane Eyre

A character, usually female, who describes herself as homely, ugly or unattractive, or is described as such by another character or the author. These types of characters tend to go one of three ways;

The character really isn't plain at all and comes to this realization herself or it is pointed out by another character. This type of Plain Jane could have been Beautiful All Along or grown up nicely as the story progressed.
The girl in question really is homely, but compensates for her looks with her skill, smarts or heart. This type seems to acknowledge her unattractiveness, but does nothing to better her appearance and couldn't care less. This type of Jane is usually a Tomboy or a working girl. Usually ends with a "Don't judge a book by its cover" Aesop, but not always.
The Jane is very aware of her "ugliness" and uses it as a reason to Wangst and get attention from others. This more often than not can result in "I Just Want to Be Beautiful".

The Jane can also be the Butt Monkey of the story because of her looks and used for comedy. If the Jane is only considered ugly in canon, then she may suffer from a case of Hollywood Homely.

Compare Blessed with Suck, when Jane's plainness acts as an asset, and Ugly Cute. Contrast The Beautiful Elite and So Beautiful It's a Curse.

Examples of Plain Jane include:

Anime and Manga

Sunako Nakahara from The Wallflower/Yamato Nadeshiko Shichi Henge
Kisaragi from Elfen Lied. Illustrated in a flash back only in the manga, where young Kisaragi overhears two boys talking about how they wouldn't date her because she wasn't pretty enough.

Fan Fiction

Ivy Malfoy/Potter from Potter's Pentagon. She Cleans Up Nicely but usually chooses not to.

Film

Penny from The Rescuers .
Mattie Ross from the 2010 remake of True Grit, as gently put by Leboeuf.
Elizabeth Abbot from The Curious Case of Benjamin Button is described as plain as paper, but is portrayed by Tilda Swinton. So...
Wendy Torrence in The Shining.

Literature

Most likely the Trope Namer, Jane Eyre. She not only tells herself she's unattractive, but most of the other characters do as well. Mr. Rochester also qualifies as a rare male example.
Mary from The Secret Garden. She is described as an ugly and stern child, but becomes somewhat prettier as the novel progresses and she becomes happier.
Harry Potter's friend Hermione Granger is first described as frizzy-haired, buck-toothed and shrill, but she eventually outgrows it.
Biddy from Great Expectations.
Catherine Sloper in Washington Square is always described as plain. The narrator and other characters describe her as having the kind of looks that would be better suited to an older woman than a 20 year old, making her perhaps a delayed version of She's All Grown Up.
Sonea from The Black Magician Trilogy describes herself as being average looking, but she doesn't lack for male attention, and is regarded as attractive by those same males.
Opal Cowan from the Storm books sees herself as plain, especially compared with previous protagonist Yelena, but she proves just as appealing to men, if not more so. The book cover also shows her as being very attractive.