Dib's Mother

Dib has No Mother
Although we would all love to hear the tragic backstory of Dib and his mother, the most logical is that Dib just never had one. She is never mentioned in the show, not even in flashbacks or pictures. This theory couples well with the theory that Dib is a flawed clone of Professor Membrane; one that was suppose to be smarter than him; thus resulting in Dib's large head.

Dib's Mother is an Alien
See: Dib isn't human

One theory is that Dib's mother is an alien, though it's not as common as the theory that Professor Membrane is an Alien. The theory is generally used to explain why Dib has such a big head and why Professor Membrane discourages Dib from looking into Aliens for fear that he'll try to learn more about his mother.

Paranormal Death
Some believe that Dib's mother died because of a paranormal accident, whether because of an accident or because she was interested in the paranormal herself and was killed during an investigation. This may explain why Dib was so obsessed with the paranormal, why Professor Membrane tries to push paranormal things away, and why Gaz wants nothing to do with the paranormal (either because she was too young to remember, or because she has already moved on).

Regular Death
Instead of being killed in a supernatural, unexplainable way, some believe she just died of an illness or natural causes. Some even say she committed suicide, not being able to handle the thought that her own son might be insane.

Dib's Mother is not Gaz's Mother
One theory is that Gaz is Dib's half-sister or step sister, and Gaz's mother is a supernatural entity. If Dib is a clone of membrane then Gaz's mother would be the only mother Dib knows.

Dib's Mother Was Abusive
Although unpopular, there are people who think that maybe Dib's mother isn't seen because Professor Membrane had to leave her to protect himself and his kids. Fanfiction writers tend to feature this in fiction where Gaz's mother is a supernatural entity such as a demon.