They first appeared in Uncanny X-Men Annual #12 and were created by Chris Claremont and Art Adams.
In Uncanny X-Men Annual #10 (also by Chris Claremont and Art Adams), Mojo had de-aged the X-Men (Nightcrawler, Shadowcat, Wolverine, Rogue, Magneto, Psylocke, Colossus, Storm and Longshot) into children; this is what most likely inspired the creation of the X-Babies.
There has also been a similar team instead based on the Avengers, called the Mitey 'Vengers, who appeared in the X-Babies Reborn one-shot.
Several incarnations of the X-Babies are friendly with Ricochet Rita, the good past-self of the villain Spiral.
This version had a much more expansive roster, including members of the New Mutants, X-Force, X-Factor, Generation X, Excalibur, the Xavier Institute student body, X-Statix, and the Chicago Morlocks.
As a tie-in to the Avengers Vs. X-Men event, a spoof comic called A-Babies Vs. X-Babies #1 (2012) has been released.