Currently in the comics he is part of the Teen Titans.
in the cartoon Batman Beyond/Static Shock/Justice League crossover when he is much much older he is part of the Justice League.

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Wasn’t there a cartoon called Justice unlimted or something before?

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None of them. During JLU’s tenure, the producers and writers were under a ‘Bat Embargo’. Since the newer series ‘The Batman’ was under full swing, the only character from the Batman Family that JLU was allowed to use was Batman himself. So no Batgirl, no Alfred, no Robin. Nightwing was allowed a very brief cameo in the episode ‘Girl Fight’, but that was it.

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