The Ninth and Tenth Doctors have never encountered each other in the television series.
In "Prisoners of Time" (IDW comic story), the first Eleven Doctors all meet near the end of the comic. However, it is possible that all but the Eleventh Doctor will forget this meeting, based on information about multi-Doctor events given in "The Day of the Doctor".
The Ninth and Tenth Doctors have not met, but David Tennant and Christopher Eccleston acted together in the film Jude years before either was on Doctor Who. They also share an American accent coach and according to a 2009 interview with Tennant have had tea together.