I'm feeling inspired by the absolutely TOO FUN ST:TNG/Dr. Who mini-series currently out. How's this for a fun idea of a Batman universe/Dr. Who universe crossover:
The pesky Master has made his way to Gotham and has joined forces with Two-Face to bring up some chaos to attract the Doctor's attention, little does he know that this also attracts the attention of Batman and Batgirl! Batman and Batgirl find themselves quickly outmatched by the dangerous Master but the TARDIS appears and out comes the Doctor and Amy Pond to help.
Two-Face winds up stealing a coin artifact from the Master that has special time bending properties, and Batman elicits the aid of the expert thief Catwoman to help get it back. As insurance though the Doctor also "steps out" briefly to bring in HIS expert archeologist aka River Song to also help get back the artifact.
Three teams set out, Batman and the Doctor to find the Master, Batgirl and Amy Pond to stall and/or take out Two-Face's goons who have been influenced by the artifact, and Catwoman and River Song to steal back the alien coin from Two-Face.
Would this be a fun series or what! Of course the initial inspiration was seeing the two red heads of Batgirl and Amy Pond together