Which characters would you have liked to see interact together in the same episode or movie, whom we did not see interact? For example, I was disappointed when Q and Odo did not share time together in "Q-Less." I thought that would have been interesting. But I can think of many other examples: Lore and Q, Q and Douwd, Organian and Trelane, etc. Characters don't have to be from the same series.
EMH: "You're prejudiced against holographic beings." McCoy: "I'm a doctor, not a laser-Floyd concert."
Lwaxana and Nurse Chapel. j/k I would have loved an episode where Ro turns up at DS9 just too see how well (or badly) she and Kira would have gotten along. I'd also like to see what Q would do with Charlie Evans. Or what Charlie Evans would do with Wesley Crusher.
Janice Rand and Sulu. They had great chemistry in the Man Trap and I think it would have rounded out both characters. Kim and the twins. Not in a pervy way but they were astrophysicists and the only scientist Voyager had apart from Janeway was an astrobiologist. Ensign Ro and everyone. Janeway and Q. What a lovely couple.
Some of these interactions actually happened, though. I think Lore and Armus would be an interesting pairing, also.
We got a bit of character "interaction" that I'd always wanted to see in the new movie: Spoiler: Into Darkness Spock vs. Khan.
M5 and Nomad, just to see which of them could take control over the Enterprise, with or without destroying the other, in the Mirror Universe, while battling the Doomsday Machine with the Enterprise. Also, Gary Mitchell (after the accident at the edge of the galaxy) and the Talosians. Navigator NCC-2120 USS Entente /\