Not really, they are all part of "Star Trek", as are your own excellent DTI books. I'm asking about books not about Star Trek but use the universe as a backdrop. For example a detective story on Alpha Centauri, a hospital drama on Federation Earth, a romance on Kronos
That's still Star Trek, dude. It's just not Starfleet. And no, you'll never find a Trek novel that doesn't feature a single canon character. Even Vanguard has M'Benga. The closest thing to what you're describing is The Case of the Colonist's Corpse which is a Perry Mason-esque murder mystery pastiche starring Samuel T. Cogley. But if you want a book that doesn't focus on Starfleet, there's Rising Sun which is told from Jake Sisko's perspective but is mainly about a motley freighter crew in the Gamma Quadrant. There's also KRAD's IKS Gorkon/Klingon Empire series. If you want books that don't focus on regular characters from the TV series and movies, try the novel-only series like Vanguard. I'd say New Frontier, but that, by design, has a number of TNG guest stars become regulars in that series, Shelby, Lefler, Selar, and so forth. But you're not really going to find a novel that doesn't feature Starfleet in some way and also doesn't feature canon characters. That's just the nature of a media tie-in. If you want to read stuff set in the Trek universe that doesn't feature canon characters at all, there are people who can point you to some fairly well-written fan fiction (just not in this particular sub-forum), or towards some sims/rpgs that are essentially collaborative writing groups. I've been in several over the years that were set on civilian vessels or colonies and had little to no interaction with Starfleet.
Here's a good example of a non Star Trek character involved with the Star Trek continuity... Spoiler: Jamie Sommers Bionic Woman Jamie Sommers was a Human American that was a former tennis player. In 1986, Sommers was serving as United States President Ronald Reagan's translator while he was in Reykjavik, Iceland meeting with Soviet General Secretary Mikhail Gorbachev to discuss the reduction of nuclear weapons in their country's arsenals. (TOS novel: The Rise and Fall of Khan Noonien Singh, Volume 1) Awesome book by the way. This seems to be a reference to Jaime Sommers of The Bionic Woman. From Memory Beta
Oh, I was going by Memory Beta and I didn't notice Worf, Troi, or Uhura on the list. I did see Curzon, but I wasn't sure how exactly he would be categorized on the main-recurring-new character spectrum.
Except that Star Trek is the universe, not any one part of it. Every sequel, prequel, and spinoff series has included Star Trek as part of the title. Enterprise was without it for the first two seasons, but then it was retitled Star Trek: Enterprise for the name recognition. If all those different series set in different times and places and featuring different people were all Star Trek, then there's no real way to define something that's part of the universe but doesn't fall under the ST label.
Would still like to see a story about a descendant of Machii Isao go to Qo'nos looking to find (and defeat) the greatest Bat'leth wielder of the age.
I just finished that book this evening! So good! What an interesting species the Andorians have become.
A significant portion of Diane Duane's novel Spock's World deals with events on pre-Federation Vulcan. In a way, it's like two books in one, since you can read the Vulcan stuff as a series of short stories without reading the 23rd century material, or vice-versa. Other than that and what's already been mentioned, you might want to check out what's available in fanfic. There's plenty out there that involves the Federation (or other places known to the Federation) but isn't Starfleet-centric or uses all-canon characters.
Indeed! I was yearning that book since December 1979 - glimpses of Andorians in publicity material, flashback images of Andorians in TOS and TAS, and waiting through the next few years for "Star Trek: The Motion Picture II". I knew in my gut that we'd never get an entire novel set on Andor, but now there's been "Paradigm" and "Paths of Disharmony". (And "Ex Machina", which is essentially "Star Trek: The Motion Picture II".)
I'm still waiting for a miniseries about World War III. That would not, technically speaking, be Star Trek, but it'd be in that universe.
I once, as an exercise for a writing class at a local junior college, wrote a SS about the fauna and former sentients of M113, in the form of a news interview with the son of Robert and Nancy Crater (although Captain Sulu appears in it). And I also wrote a Borg origin SS, for that same class (although V'GER appears in that one). Both, of course, unpublished (except that I think one of them might have gone into the class anthology). Now if you'd be happy with a milieu that's a lot like ST, (and you like ADF's novelizations), then I humbly suggest ADF's Humanx Commonwealth books.
As an update thanks for all the recommendations, i completed The Final Reflection a few days ago, excellent book. Its a pity the TOS Klingons couldn't have lived on alongside the film/TNG headbanger variety. A dual species empire, would have made the forehead question simpler anyway. Now on Articles... which is very good too. I guess we could do with an updated version of this nowadays.