|24: Godel, Escher, Kurt Halsey
Megan is a stick figure character in xkcd. She is the second-most frequently appearing character, after Cueball, and the most frequently appearing female character. She does not necessarily always represent the same character from comic to comic. She is essentially the female equivalent of Cueball, representing the every-woman to his everyman. This is less clear than for Cueball as there are several comics where there are multiple Cueball-like figures, any of whom could be called Cueball. There are very few comics where this happens with Megan-like characters, with the few including 139: I Have Owned Two Electric Skateboards, 173: Movie Seating, 1409: Query, 1496: Art Project, 430: Every Damn Morning, 2040: Sibling-in-Law, and in 1951: Super Bowl Watch Party.
Of course, she also appears several times in some of the comics with large drawings, like 1110: Click and Drag. Often this should be seen as different small comics, where there is just one Megan in each story. In 1608: Hoverboard, however, there are two identical Megans at the bottom rear end of the Destroyer, where one is talking to the other. As opposed to with Cueball, an example where this is a problem for Megan has yet to be found.
Megan does sometimes appear to have slightly specific personality traits; she has quite odd habits and is sometimes shown to be very focused and intent on a goal. However, as explained above this is not a general rule for a given Megan character.
Explain xkcd originally referred to this character as "Cutie" (complementing "Cueball" with a matching first syllable). But then a "Cutie" was given a specific name, Megan, in 159: Boombox and later in for instance 215: Letting Go, 420: Jealousy, 478: The Staple Madness, and 654: Nachos. The name was also used without displaying a drawing of Megan in 596: Latitude and in the title text of 627: Tech Support Cheat Sheet. The name Cutie was then changed to Megan. If this rule should be followed generally, then Cueball should be re-named Rob after 276: Fixed Width (and the other 12 times a Cueball has been named Rob in total). But as mentioned above this was not to be.
She can also be drawn under a different name as in 672: Suggestions, where a sexy image of her, hair hanging loose over her face, is called Susie. And in 1221: Nomenclature Megan is called Mrs. Whatsit in the transcript provided in the comic source. In 734: Outbreak Cueball and Megan are named Ryan and Laura, but that is a movie, so they could be actors called Cueball and Megan in real life. A character that looked a lot like Megan, but with somewhat longer hair and a much meaner attitude, was distinguished from her as Black Hat's girlfriend Danish. A similar long-haired version of Megan also appeared in 1730: Starshade, although without the attitude.
Early comics often feature Megan-style characters who may or may not be identified as Megan. Randall appears not to have standardized his character lineup early in the comic's run, and as a result, certain early female characters sometimes have similar hair to Megan, but some different features. The name (or even pseudonym) "Megan" may be reference to a lost love of Randall's, given that he wrote a passive-aggressive toast for Megan's wedding in 420: Jealousy about how he was madly still in love with her, put across in a way that would generally ruin the day for everyone involved. We also see this earlier in 215: Letting Go. Several of the comics about cancer have Megan representing Randall's fiancée and later wife.
Megan is distinguished by her black shoulder-length hair which generally appears to be parted in the middle in front and is draped behind what are presumably her (undrawn) ears. It is shorter than the character of similar appearance, Danish. Megan also tends to behave less defiantly than Danish does.
Megan's age is sometimes given, like in 1409: Query, we learn that she is 30 or younger, implying that she was born in 1983-84, and in 630: Time Travel, we learn she was born in 1983 (born after August 14). But in 2178: Expiration Date High Score, we can calculate that she was born in 1981-82 which is slightly different.