In terms of trek/Dr. Who cross-overs, for the artists out there:
TOS meets fourth Doctor
Tennant should have been on Enterprise-D (more work with Pat)
Matt Smith with JJ and Pine.
It gets a bit harder after that.
Hartnell on the Orbit Jet.
Second Doctor on Lost in space or the Time Tunnel
Third Doctor On Voyage to the Bottom of the Sea...or UFO
Fifth Doctor in Buck Rogers with Erin Grey
Sixth Doctor on Red Dwarf of course.
Seventh Doctor...hmm NuBSG--Stargate--or, of all things Game of Thrones.
Eighth on Space Above and beyond
Ninth in Alien