Just a quick question: I'm fairly new to Stack Exchange, so I was wondering why people are down-voting my question, just so I don't make the same mistake in the future. Thanks!

It wasn't just the spinoff series--- the original series recycled actors also. Diana Muldaur, Marc Lenard, Morgan Woodard and Majel Barrett are the more memorable ones, but there are several others scattered across small roles. Actors in recurring roles were more surprising than the recycled ones.

@KyleJones Ok, thanks, I hadn't noticed that before, I'll have to re-watch the Original Series!

You probably got downvoted because actor recycling is very, very common in episodic television and it is always done with no in-universe explanation. It's a peculiar thing that is simply put aside and taken for granted, like why comic strip characters always wear the same clothes and never age.

They did, in-universe, specifically recognise the similarity between Tasha Yar and Sela, both played by Denise Crosby. I'll accept that's a special case though.

Ha, knew I shouldn't have used "always" on the Internet.

Also in Next Gen Michelle Forbes played an alien before returning to play Ro Laren.

@KyleJones ok, that makes sense, thanks!

I believe there is also a point made to retcon Tim Russ to be Tuvok (Voyager) on the bridge of the Enterprise-B in the film Generations (can't recall where though, book, etc..._

@NKCampbell: The Voyager episode Flashback puts him on the Excelsior during the events of Star Trek VI, although I’m not sure if that episode contradicts the idea of him serving on the Enterprise B. (He may have said that he left Starfleet shortly afterwards.) Mr Russ, of course, also got Vulcan nerve-pinched by Picard in Next Gen’s Die Hard homage Starship Mine.

Russ was also a Klingon on the Die Hard on Deep Space Nine episode as well

@PaulD.Waite, NKCampbell: Tim Russ did not play Tuvok on the Enterprise-B. It can be quite clearly seen that he does not have Vulcan ears, for example (movies.trekcore.com/gallery/albums/generations/ch2/gen0155.‌​jpg) and his appearances are also discussed at some length in this SE question: scifi.stackexchange.com/q/31779/68434

The closest thing to in-universe would have been in the DS9 episode The Dogs of War (S07/E24) where Jeffrey Combs played both Weyoun and Brunt in the same episode. In an interview Combs mentioned that he wanted the two characters to cross on the Promenade turn around and look at each other then continue walking off. The idea never made it to film though.

@Buildstarted: goddamnit. That would have been glorious.

I always enjoy seeing the same actors turning up in other Sci-Fi TV/Movie universes. Enjoy the fact that Quark was played by the same actor as the headteacher in Buffy, my favorite crossover of all time is Jenette Goldstein who played Vasquez (Aliens), Janelle (Jon Connor's Step-mother in T2) and also played a Science Officer in Star Trek: First Contact.

@KyleJones: "often" is not the same as "always". The first episode of series 8 of Doctor Who addressed the fact that Peter Capaldi, playing the Doctor, had already appeared as a character actor in an earlier season in a in-universe way. This was silly, but hey, it's Doctor Who.

You really think Brunt looks like Weyoun?

It's not that I think they look alike, but they were played by the same actor.

Especially with the complications it caused, for example Brunt and Weyoun once appeared in the same episode together. Thanks for asking for clarification though, it helps me to improve the question.