Over the course of the last sixty years, Robin has had many different origins, most have been similar, yet a little different to change with the times. Below, you will find some of the different bios, that there has been.
Dick Grayson of Earth-2
After Bruce's death, Dick thought about taking on the role of Batman, but decided against it. He did don the cowel once to stop an aging Joker, but returned to being Robin afterwards.
At around 58 years old, Dick died a heroic death as Robin while struggling to save others during the Crisis on Infinite Earths.
Dick Grayson of Earth-1
[This Dick Grayson's early history was almost identical to that of the Earth-2 Dick Grayson.]
The information above was taken from the recent Robin Year One and Dick's Secret Origin story, along with some New Titans issues amongst others.
Full Name: Richard (Dick) John Grayson
Dick Grayson was a member of the Flying Garrison’s, a famous trapeze act made up of John and Mary Grayson (his mother and father), from the age of five. He was with them for the next five years, twice nightly, until one night, just before his tenth birthday as he waited to go on, disaster struck. While his mother and father were performing their famous triple somersault, their trapeze snapped and they fell to their deaths. Learn more about Dick Grayson as Nightwing
Robin has been played by four diffrent people. Click on the one you'd like to know more about.
Born c.1927.
Started career in 1940.
First comic book published in 1940.
Dick Grayson was a circus prodigy. His parents were stars on the high wire and trapeze, and he joined them in the act at an early age. But Boss Zucco, a Gotham gangster, was trying to extort money from the circus by sabatoge. Dick witnessed the death of his parents when a trapeze that Zucco had tampered with broke during the show.
Now an orphan, Dick was taken in by millionare Bruce Wayne. Bruce revealed that he was secretly the Batman, and offered to help Dick bring Zucco to justice. Soon Dick had a costumed crimefighting identity based in part on his favorite story book hero, Robin Hood. As Robin "the Boy Wonder", Dick became Batman's junior partner, bringing first his parents' killer to justice, then many more criminals.
Perhaps it was the fact that Zucco was brought in so soon that prevented Dick from becoming as grim a figure as Bruce. As a superhero, Dick was more prone to swashbuckling and laughing in the midst of battle. His acrobatic skills were such that he taught Batman a thing or two, and coupled with the martial arts he learned from Batman, Robin's speed and agility often allowed him to make bad guys look like lumbering clutzes. Some of Robin's lightness of heart seemed to rub off onto Batman, making him seem less predatory and more heroic.
Dick eventually went to law school and into legal practice, but continued to act as Robin. He modified the costume a bit, and the epithet "Boy Wonder" certainly ceased to apply, but he was still Robin. As Bruce became less active as Batman, Robin took on more of the heroic duties in Gotham, and took Batman's place in the Justice Society of America. Eventually, Dick also began to spend less time in costume, as Bruce's daughter Helena was taking on part of the load as the Huntress.
Born: floating date between c.1942 and c.1962.
Started career: floating date between c.1955 and c.1975
First comic book not clearly determined.
The transition from Golden Age to Siver Age (later designated Earth-2 and Earth-1) versions was unintentional, and had no clear splitting point. Robin's early history was much more consistant between versions, but in some cases, character traits and continuity events that would later be ascribed specifically to different versions of Robin had actually been associated with a single Robin in a past story. Once the Earth 2 & 1 concept had been developed, the Earth-2 Robin was linked with the original appearance date while the Earth-1 Robin was kept roughly static by floating his past history. So, whenever the Earth-1 continuity comic book was published, Robin was born about 13-18 years before, and commenced his career at at around 13. Later Earth-1 stories gradually let Dick Grayson age from a child to a young adult, first as a more mature Robin, then as Nightwing he must've aged to his early 20s.
When Dick went off to college, he began to act as Robin more independantly from Batman. In time, he became affiliated with a group of young heroes called the Teen Titans (later just the Titans). He eventually left school (much to Bruce Wayne's consternation) and adopted the costumed identity of Nightwing, which was almost a cross between the Batman and Robin costumes.
Parents: John and Mary Garyson, deceased. Placed in the custody of Bruce Wayne until he was of legal age.
Birthdate: March 21st (The First Day Of Spring)
Height: 5'10"
Weight: 175 lbs.
Hair: Black
Eyes: Blue 
Occupation: Police Officer by day, vigilante by night.
Place of residence: Blüdhaven, a whaling town just south of Gotham City.
Particular Skills: Trained as a circus performer from an early age. Natural athlete and highly trained detective. Master of several martial arts but favors Aikido and Jeet-Kune-Do.
Hobbies: Writing fiction when he has the time.
First Appearance: Detective Comics #38 (As Robin), New Teen Titans #39 (As Nightwing)
Not long afterwards, Dick was taken from Haley’s Circus and put into Gotham City's Youth Center waiting to be fostered. Unfortunately, this was also where they put the underage criminals, who liked to beat up on the new kids. Covered in bruises and realizing he was stuck in a system that had forgotten about him, Dick made his escape. He climbed up a chimney to the roof, which is where he first bumped into the Batman. Batman told him he was investigating the murder of the Flying Graysons and that he had found organic acid on the rope that mimicked natural wear and made it look like an accident. Batman also told Dick that he would have to stay at the home for the time being - he couldn't help a fugitive - but he promised he wouldn't be there long.
The next day, Dick was fostered by Bruce Wayne, a leading Gotham citizen. He was given everything he wanted, but underneath he felt like a Christmas puppy - like he'd been taken in because Bruce felt sorry for him. Haley’s Circus was back in Gotham again, and since there was no sign of the Batman, Dick decided to do some investigating of his own.
He overheard some gangsters working for a Boss Zucco trying to blackmail Pop Haley, the owner of the circus. They told him that if he didn't pay them, there might be more accidents like the Graysons. At this, Pop lost his temper and hit one of them. The others gunned down Pop in cold blood, before he had a chance to run. Loosing his temper, Dick jumped into the fray, but didn't fair well. The goons were about to execute Dick as well, when they were hit with Batarangs. The last thing Dick saw before he passed out was the Batman taking out the thugs.
Dick awoke to find himself in a bed in the Batcave. He told Dick that someone from the circus had murdered his parents for Boss Zucco and that he needed Dick's knowledge of the circus to catch him. Dick followed the Batman up some stairs that led to a grandfather clock in Wayne Manor. Batman revealed to Dick that he was in fact Bruce Wayne, much to the surprise of Alfred!
Over the next six months Dick worked long hours with Bruce training in Martial Arts and other physical skills, while Alfred tutored him with regular school work, as well as extra studies in forensics, criminology and police sciences. Shortly before his eleventh birthday Dick became Batman's junior partner. He didn't want to be a junior Batman and asked to adopt a different persona. He chose Robin - a nickname his mother had for him. 
The Batman and Robin team became a legend, but it wasn't until months later that they caught up with Boss Zucco. After been knocked out by Robin, Zucco awoke in a car attached to a crane high above the street. Zucco confessed everything when Batman convinced him that he was quite willing to drop him.
The lion tamer, Rutledge, had owed lots of money to Zucco's loan sharks and by killing the Graysons had paid off his debt. His brother worked in the furniture business and so he had easy access to organic acids.
Robin confronted him alone with this knowledge and Rutledge ran - straight into the tiger cage, where he was killed.
The Batman and Robin team continued, but Dick started to realize that he wasn't the same as Bruce. He wasn't so obsessed and single-minded. It was about this time that Dick joined with other kid sidekicks - Speedy, Wonder Girl, Kid Flash & Aqualad - to form the Teen Titans. Bruce and Dick had started to drift apart, and when the original Titans split, Dick left Wayne Manor and headed for college. 
Unfortunately, while Robin's solo career was going well, Dick's academic career went rather poorly and he eventually dropped out of school, much to Bruce's anger and disappointment. Loosing direction with his life, Dick wasn't entirely satisfied with Robin's career either. It was at this point that the Titans reformed. As the team started to click, Dick realized that he'd found his true calling in life.
Later, when out on a case with Batman, Dick was shot through the shoulder by the Joker and fell from the roof of a building. He was badly hurt and although Batman caught the Joker, he was very shaken by what had happened. He decided that it was too dangerous to have a teenage sidekick and that Robin was no more.
Parts of this bio came from:
Robin - The Unioffical Website
Big Dave's