Usually when I find TV mash-ups via Youtube, they're basically just scenes from one show set to the theme song of another. (My favorite of these has 'Doctor Who' set to the music of 'Quantum Leap'; as Nine would have said, "It's fantastic!")
But here's one that creates its own little story and really leaves me hankering for more!
"DOCTOR WHO MEETS STAR TREK: THE NEXT GENERATION"
Any experts on 'Doctor Who' chronology want to take a shot as to when in the timeline this might work best? It can't be after "Earthshock" unless you then come up with a way to splain how the Enterprise went back to the Age of the Dinosaurs and rescued Adric. But it does have to be after Turlough's first declared intention to go home (which doesn't have to have ever been televised.)