(I've had this answer ready for sometime, it's just that RL has been being *real*.)
I'm presuming the question means two canons colliding, not shifting characters from one over to another.
Star Trek's set up allows for so many cross-overs because they're 'seeking out new worlds and new civilisations' so they can run into people.
And lots of other sci-fi shows are full of people running away from things.
The obvious show to cross over would be Blake's 7, just for the look of sheer disbelief on Blake or Avon's face when a Federation captain goes, 'the Federation are friendly'. Yes, precisely *that* look. I suspect that Mal Reynolds's look would be similar.
Or possibly Crichton et al wormholing into Star Trek and really liking it but having to go back to their 'verse to stop Scorpius.
Day 1 -
Which Star Trek series is your favorite?Day 2 -
Who is your favorite character?Day 3 -
Who is your least favorite character?Day 4 -
What was the first episode/movie you watched?Day 5 -
What was the first Star Trek series you watched?Day 6 -
Your favorite canon pairing?Day 7 -
Your favorite non-canon pairing?Day 8 -
Your favorite actor/actress? (Not the same as character.)Day 9 -
What's your favorite episode?Day 10 -
What's your favorite species?Day 11 -
What's your least favorite species?Day 12 -
Favourite Funny MomentDay 13 -
What's your favorite dramatic moment?Day 14 -
What's your favorite Star Trek quote?Day 15 -
How did you get into Star Trek?Day 16 -
Are you involved with Star Trek fandom?Day 17 -
Have you read any of the books? If so, which ones?Day 18 -
If you could be any species in the Star Trek universe, what would you be?Day 19 -
How did the Star Trek reboot affect you?Day 20 -
Favourite One-Off (Non-Recurring) CharacterDay 21 -
Which Star Trek food would you want to try at least once?Day 22 -
Which Star Trek world would you want to visit at least onceDay 23 -
Is there anything you'd want to change about Star Trek? Why?Day 24 -
Is there anything about Star Trek that has disappointed you?Day 25 -
How has Star Trek changed you?Day 26 -
Lots of Star Trek Parodies out there. Which do you dig? Day 28 - Your favourite friendship in Star Trek?
Day 29 - If you could tell Gene Roddenberry one thing, Star Trek related or not, what would it be?