Okay, so, back in 2004, it seems that there were plans to have a Doctor Who/Star Trek crossover. However Enterprise, the Star Trek series playing at the time, was axed before it could have happened.
Just to think that it could have happened makes me squee with total fangirl delight. Ah, the possibilities!!!
The information was taken from Doctor Who The Writer's Tale: The Final Chapter just published in the UK.
SFX made a list of 20 things they learned from the reading of the book.
Amongst other interesting points made was that there was a line that was ultimately cut from the scene where the Doctor talks to Wilf on the Vinvocci's spaceship. Supposedly the Doctor would have told Wilf that he “was half-human back in 1999 for a couple of days.” This line would have referred to the 1996 Paul McGann Doctor Who movie.
Go here to read the list.