Robin, Kid Flash and Wonder Girl had been members for a long time....but, what about the new kids of Changeling, Raven, Cyborg and Starfire?
They all had history as well, some more than others.....
Changing the Beast
original Teen Titans in Teen Titans #6 (November-December, 1966), but is also unable to join them regularly....at least until Mento (Steve Dayton) and Elasti-Girl (Rita Farr) take custody of Gar in Doom Patrol #110 (March, 1967), though the Chief never does get around to making Beast Boy a member, as he gets involved in trying to rehabilitate Brotherhood of Evil member Madame Rouge (which doesn't work out). Gar at least continues to work with the team and Mento until Doom Patrol #120 (July-August, 1968), and Madame Rogue (with the help of Nazi Captain Zahl, kills the team in the next issue).
Lilith, Hawk & Dove, Bat-Girl and Golden Eagle to form Titans West, which lasts for 2 more issues before the team slowly fades away, making Beast Boy a short lived Teen Titan.
Robotman, as well as the Brotherhood of Evil) to capture the killers of the Doom Patrol, as well as getting a new girlfriend in Terra (a girl who can literally move the Earth....though Gar's involvement with her turns tragic due to the interference of Titan foes, Deathstroke the Terminator and the H.I.V.E.).
Devil at the Door
Bits and Pieces
The above relates the original DC Universe origin of Cyborg, as Victor told it in the Tales of the New Teen Titans #1 (June, 1982) by Marv Wolfman, George Perez and Brett Breeding.
Fighting for Freedom
Koriand'r took advantage, and freed them both, only to have Komand'r return Kori to the Gordanians (all revealed in flashback in the Tales of the New Teen Titans #4 of September, 1982, by Wolfman, Perez and Ernie Colon). With her new powers, Kori was able to escape, heading to the planet Earth....and her first meeting with Robin and the rest of the Teen Titans in New Teen Titans #1 (November, 1980).
Dick, Wally and Donna) came about because of foes they faced like H.I.V.E., Deathstroke the Terminator, the Fearsome Five, the Brotherhood of Evil, Blackfire, Cheshire and Brother Blood, and before learning more of the future of these Titans, more of these villains has to be revealed as well....but, for now, remember these Titans....Together!