Madotsuki (pronounced Ma-doht-ski) is the player character in Yume Nikki. Fans speculate that she is young -- anywhere from nine to fourteen years old -- although arguments can be made for any age. The fact that she is depicted in a chibi-like style implies that she is young. She is probably no younger than sixteen, however, since she lives alone. Madotsuki is the only character in Yume Nikki with an official name, since characters require a name for the menu screen in RPG Maker games.
As with virtually everything else in the game, Madotsuki's identity and life are a mystery. Only what can be seen in-game can be considered canon. The only thing that is generally accepted among fans is the that Madotsuki is a hikikomori, or shut-in. This is supported by her refusal to leave her room -- if a player attempts to leave, she merely shakes her head.
Real life
Madotsuki doesn't have much to do in her room. Her television set doesn't receive any channels (the deprecation of analog signals would explain the test screen, a possible prediction from 2004), so she can only play her single game, Nasu. She can go outside on the balcony, but the balcony itself must be rather high, and her view always seems to be blocked by fog.
Madotsuki's dreams
Elements in Madotsuki's dream world seem to hint at her emotional state. Some effects seem to show her unhappiness. The knife, in particular, appears to hint at her misery. However, the player ultimately controls Madotsuki -- it is unknown whether she would use the knife on her own.
Since many dreams are disturbing when shared, Madotsuki may just be a typical lucid dreamer trying to find a release from her sadness by exploiting her dreams for fun and self discovery.
Fan speculation
Name
The word "Madotsuki" (窓付き) means "window", as in an aperture or peep-hole. It is not a common Japanese name, and in fact, it may not even be the character's name at all. It could be thought of as being more a description of the character as the player's window into the dream world rather than a literal name. It could also be a way to preserve the game's theme of loneliness by giving the character a functional, dehumanizing name, rather than a personal name.
Mental illness
It is possible that Madotsuki is depressed, and that her dreams are caused by her medication. (Specifically, she could be experiencing REM rebound.) Depression would explain her images of despair, hopelessness, and end-game tendencies.
Gender issues
Due to the recurring images of orifices, blood, and a road with womb-like creatures, and the fact that Madotsuki uses both the men's and women's restrooms in her dreams without hesitation, Madotsuki may feel gender troubled. This can be taken in either direction. She could be a male to female transgender living as a female or a female who feels male. However, it seems to lean toward MTF due to KyuuKyuu-Kun, who looks like a phallus followed by a disturbing face in the shape of a penis head, complete with a possible urethra.
Accident
It is thought that Madotsuki was involved in a traffic accident in her past -- the same accident that Monoko is speculated to have been in. The bloated abdomens found in Madotsuki's dreams may be images of her decapitated and pregnant mother. The severed heads in the monochrome world could be people who died in the accident and may perhaps include Madotsuki's mother and father. Monoe may be a deceased sibling.
The Severed Head effect may be linked to the decapitated mother and father in the front of the vehicle. Stoplight could be linked to the accident happening at a stoplight.