Dogbert is, rather non-amazingly, a dog in the Dilbert comic strips by Scott Adams. Although Dilbert chose him as a pet in a series of unpublished strips Dogbert couldn't be called Dilbert's dog. Dogbert simply chooses to live with him.
Dogbert is small, round and has little legs. He also wears glasses, so he takes on a piece of Dilbert. His ears also look quite cute when they flay up through fear or shouting at people. He once used this trait to get everything he wanted by keeping his ears up all day and protesting he looked so cute, you couldn't deny him anything. You see, Dogbert is actually a megalomaniac, whose sole intention is to conquer the world, and turn all humans (who don't subscribe to the Dogbert's Ruling Class mailing list) into his own personal slaves. Adams says he uses Dogbert to say all the things he wishes he could, but can't for fear of retribution. There is, at the time of writing, no precedent to say that passing on authorial opinions onto a fictional cartoon dog will hold up in the court of law.
His beginnings can be attributed to Adam's childhood dog, Lucy. In the book "Seven Years of Highly Defective People" he says "Lucy never came once when I called...she did absolutely nothing except what she wanted to do."
Dogbert takes on a lot of different occupations, only for his personal pleasure. My favourites include the oft-recurring Technical Support Engineer ("How may I disconnect you?") and the Network Administrator ("I can't deal with your pathetic request, I'm busy upgrading the network!"). These are often coupled with cool looking hats, such as the purple Nostradogbert turban thing. The most memorable occupation was when he became the self-proclaimed "Patron Saint of Technology" The catchphrase was "Out! Out Demons of Stupidity!" He wears a three pronged hat and waves a cool wand in an authoritive way.
He will always rescue Dilbert in a crisis, such as when Dilbert was taken hostage by accounting and when Dilbert was killed off in 1990.
To conclude, I will leave a quote from one of his dreams (I use this line with my friends/enemies/random tramps. The effects vary):
"Ha ha! I am Saint Dogbert! Line up to kiss my feet, you knaves!"
That Dogbert Origin link - http://www.dilbert.com/comics/dilbert/news_and_history/html/dogbert_origin_strips.html