All the TV series had at least some great music.
This is my copy of the TOS box set:
TOS music, with all those great episode scores, is a life-long passion for me. I'm glad to have it all, every note, and to know it is preserved in a stable format. No more fear of decaying tapes. How great is that? The show's main title is so wrapped up in my childhood, speaking as it did of a great adventure coming up, that I can't judge it objectively.
The 1973 animated series had a limited but effective selection of music cues, the bulk of which can be found in a 15-minute youtube presentation. It's less adult than TOS music, but I still have a fondness for it. And I like the main title, too.
For me, the rest of the ST series were more about intermittant musical highlights than a steady diet of memorable scores:
TNG featured some nice classical music echoing through the ship (Bach's 3rd Brandenburg Concerto, Chopin's Trio in G minor), and Picard's flute melody, dazzlingly realized on CD as the "Orchestral Suite from the Inner Light" by Jay Chattaway. My favorite full episode score is "The Best of Both Worlds" by Ron Jones. The series main title is actually my favorite version of the Goldsmith TMP theme, because it's so punchy and exciting.
I loved DS9 in first run but don't remember it well because it's been so long. A big highlight of the series would be the holosuite lounge singer Vic Fontaine (James Darren). All his numbers were great; Darren put them out on CD and it's quite listenable.
The DS9 episode "Chrysalis" had a musical number performed by the guest stars, a Do Re Mi song that they supposedly improvised. That was pretty cool.
The show's main title is grand and stately, which is fine by me, but I often wondered if something more exciting, cut together with the actors in action, would have been better for the ratings.
VOYAGER was a great show for intermittant musical highlights. Seven of Nine sang "It Can't Be Wrong" in "The Killing Game." She sang "Clementine" and "You Are My Sunshine" with the Doctor. The Doctor sang opera-style from time to time. Those scenes were always great.
ENTERPRISE struck me as the least-musical of the six shows. I don't remember anything offhand. I liked the main title song a lot until they upped the tempo in later years. That didn't work for me.