I originally started watching The Teen Titans without knowing any background at all on the tv show, or the comics. Searching for more information on the current Titans, I ran across a lot of other interesting things, that confused me. I have come to the conclusion, (thank you captian obvious!), that The current Teen Titans have been based of off their older versions of themselves.
The 1940's
I do believe it all started with Batman actually. The dark, quiet superhero lurking through the nights. Robin debuted in Detective Comics #38 (April, 1940). Soon, other major heros were getting teenage sidekicks. Aqualad - Aguaman, Kid Flash - The Flash, Wonder Girl - Wonderwoman, and many others.
The 1960's
Robin started out being 12 years old, but soon grew into his teenage years, where he met up with Aqualad, Kid Flash, and Wonder Girl, when they started the Teen Titans. Eventually, more characters like Speedy joined, and soon The hawk & the Dove, and Beast Boy became regulers in the comics. Older characters dissapeared almost completely, and the series was soon no longer connected to former comics. The series ended in 1973.
The 1980's
All the characters from the earlier series were matured slightly, names changed (Beat Boy became known as Changling), and new characters added, Raven, Cyborg and Starfire. Robin eventually abonded the name Robin, and turned to the name Nightwing. By 1988, Robin had graduated from College, and Wonder Girl had gotten married. The word 'Teen' was then dropped from their name, and The New Titans continued on until 1996. Another spin off had been running with DC's even younger characters for a while, including Superboy, and The Atom.
Picures...

BEAST BOY/ CHANGELING UNAVAILABLE
*NOTE*
All of this was written and researched by me. So don't copy!