Philip J. Fry was frozen for a thousand years and thawed in the year 3000. His entire family was dead, as was his cheating girlfriend. He literally knew no one, but it didn't bother him. In a sense, Fry was home. Like many people today, he dreamed of the future, and, even though he's technically a delivery boy, he loves his job and his new life. His best friend is a robot named Bender Bending Rodriguez (or just Bender), and he longs for an alien (or is she?) cyclops named Turanga Leela (or just Leela). Through his great great great great great (there are probably more greats) grand-nephew, he finds his job as a delivery boy.
When "Futurama" begins, Fry is, well, lazy and stupid. This doesn't change much over the course of the show, but his stupidity becomes important. As it turns out, Fry is no ordinary human. He lacks the delta brain wave making him superior but also inferior to other humans. How this happened is revealed in the episode where he, along with other crew mates, are sent back to 1947 Roswell, New Mexico. Fry's grandpa is stationed here, and Fry takes it on himself to check on his grandpa and ensure his survival. Eventually, Fry gets his grandpa, who appears to be gay, killed. So, Fry naturally comforts his grandma and one thing leads to another. In short, Fry becomes his own grandpa because he did the nasty in the pasty, resulting in his special abilities.
These abilities are put to good use when his powers make him immune to dumbing effects of the Brainspawn (giant brains that try to take over Earth and later try to destroy the universe). Fry is able to stop them using quick (but not too quick) wit. Then, he's recruited again to stop the Brainspawn from destroying the universe, which he does in a hilarious fashion. Fry also helps to save the Earth from an impending garbage ball from outer space, the common cold, and the Dark One.
His lack of thinking is often a detriment to him, but it has saved humanity multiple times. So, in a sense, it makes Fry the smartest idiot in the 31st century, and this is by design. Increasing Fry's importance in the universe allowed for more story lines to revolve around him. Also, Fry being dumb is a joke that becomes tired after a while. It's much more fun for Fry to, sometimes, be the lynchpin that saves humanity. In many ways, he is also the common man. As an outside observer, viewers are like Fry. He is the most similar to us, and, while we have no problem relating to a genuinely nice guy, relating to a consistently stupid guy is harder. These episodes where Fry is the savior of mankind make the series what it is today. So, here's to hoping that Fry continues to be the smartest idiot in the 31st century.
"Philip J. Fry" Futurama Wiki