I struggled with deciding this one and then went for the first thing that kept popping into my head. I remember beaming (excuse the pun) when newly-demoted Captain Kirk sees the Enterprise-A for the first time and says “My friends, we’ve come home.” The music swells with the original series which to this point has largely been absent from The Voyage Home soundtrack and it adds a nice happy ending for the last three films.
The end scene as they all settle into their roles on the bridge just tops it off and declares that the crew is ready to go off boldly going where no one has before again.
So that’s my pick for the happiest moment in Star Trek, there are plenty more but it’s the one that jumps to mind first.
This is part of the 30 Day Star Trek Challenge – check out the details here.