Inspired by a question Connavar had about Cherryh's works, here's a lengthy annotated list (initially taken from ISFDB but, obviously, much fiddled with - there are many lists which arrange her books in various ways but most of them seem to follow the marketing rather than actual contents) . Corrections almost certainly needed and very welcome.
It is arguable but, for the purposes of this post, I'm going to divide Cherryh's career into three phases.
1. 1976-1986
All of her work for this period was published by DAW and, except for the Ealdwood fantasy duo, was nominally part of the Union/Merchanter Alliance universe but few are particularly connected.
She began the Morgaine trilogy which is a "science fantasy" story which has a mention of a very tenuous connection to the Union/Alliance universe but has no necessary connection or reading order in relation to the other books though they are tightly connected to each other. (I regard these highly. Exile's Gate, listed below, was added in 1988.)
Morgaine Series
Gate of Ivrel (1976)
Well of Shiuan (1978)
Fires of Azeroth (1979)
Then she wrote two separate science fiction novels which are also nominally connected to the U/A but have no special order and are not connected to each other. (I think these are okay and Brothers is the lesser of the two.)
Brothers of Earth (1976)
Hunter of Worlds (1977)
Then she began the Faded Sun "trilogy" which is really a single huge novel (normal by today's standards) split into three. These are obviously tightly connected to each other but only loosely to U/A. (I regard these very highly.)
Faded Sun "Series"
The Faded Sun: Kesrith (1978)
The Faded Sun: Shon'jir (1978)
The Faded Sun: Kutath (1979)
Then she wrote two more separate novels. Hestia is barely connected to U/A and Serpent's Reach is very much a Union novel, though there are inconsistencies with some aspects of other Union novels. (Hestia is easily her single worst novel and was not reprinted during her recent omnibus reprints. Serpent's Reach is pretty good - perhaps average for Cherryh.)
Hestia (1979)
Serpent's Reach (1980)
With Downbelow Station, she won her first Best Novel Hugo and started the strict U/A sequence though even those are not as tight as Morgaine or Faded Sun. Downbelow deals with the Company wars and Merchanter's Luck is a very loose sequel with a very different focus and 40K is a Union book. (These are respectively great, very good, good and are core U/A reading. There are several followups, published 1988-1997 + 2009, listed below.)
Union/Alliance Semi-Series
Downbelow Station (1981)
Merchanter's Luck (1982)
Forty Thousand in Gehenna (1983)
Then she wrote perhaps her best singleton. This, like almost everything, is vaguely related to the U/A universe but has no real specific connection.
Wave Without a Shore (1981)
Then she began another tight series. If I recall correctly, this wasn't specifically connected to U/A at all, being "Compact Space" but it later turned out that Compact Space was another region in U/A space and some events in the U/A books are referred to (in a distant way) in the Chanur books. But they don't really have to be read in any order in relation to the other U/A books - they are in strict order relative to each other, though. (They're excellent. Chanur's Legacy, listed below, was added in 1992.)
Chanur Series
The Pride of Chanur (1982)
Chanur's Venture (1984)
The Kif Strike Back (1985)
Chanur's Homecoming (1986)
Another good singleton with vague Union mentions.
Port Eternity (1982)
A pure fantasy duo (expanded from a novella, originally - not bad for what it is).
Ealdwood Duo
The Dreamstone (1983)
The Tree of Swords and Jewels (1983)
Another pair of singletons with loose connections. Voyager includes a rather inconsistent U/A timeline. (They're both fine, though Voyager is written in a rather experimental mode.)
Voyager in Night (1984)
Cuckoo's Egg (1985)
This is the only book of this period that I haven't read. I'm not sure if it came out as a novel and then was turned into a shared world (called "Merovingen Nights") or if it was conceived as a shared world to start with. I think the latter. I think this has the usual mention that it's in the U/A universe but I'd be amazed if there's any real connection.
Angel with the Sword (1985)
Meanwhile, she released a connected collection of "dying earth" far future science fantasy tales and a collection of miscellaneous stories, including her very first Hugo winner (for Short Story), but both these collection were superseded later.
Sunfall (1981 C)
Visible Light (1986 C)
2. 1986-1993
Her second phase was published by multiple publishers and included a bunch of shared-world things, other media/marketing nonsense, and fantasy, along with some U/A books and a pointless collection.
This is a shared world with a much inferior writer (based on a solo work or two I've read). I haven't read these either. No U/A connection, as they are fantasies.
Hell Shared World Series
The Gates of Hell (1986) with Janet Morris
Kings in Hell (1987) with Janet Morris
Legions of Hell (1987)
U/A Part 2
This U/A chunk, where she switched from DAW to Warner, comes in at least four parts (and there are still three books yet to come in Part 3).
A belated Morgaine book (that is just as good as the first and makes a great finish to the series).
Exile's Gate (1988)
Cyteen is a Union book. Rimrunners is a Merchanter book. Cyteen got her her second Hugo for Novel. (It was okay but I actually enjoyed the shorter, tighter Merchanter book more.)
Cyteen (1988)
Rimrunners (1989)
A tightly connected duo of prequels set before Downbelow Station. (I like these a lot but they really need a sequel but never got one.)
Heavy Time (1991)
Hellburner (1992)
Finally, Chanur's Legacy gave the Chanur books a belated sequel like the Morgaine books. (Unlike the Morgaine books, it isn't really necessary as a final book and isn't as good, but it's still pretty good.)
Chanur's Legacy (1992)
Moving on from U/A, there's this fantasy singleton (not read).
The Paladin (1988)
Three fantasy books "with" other authors (written by them but outlined by Cherryh, or something like - not read).
A Sword of Knowledge "Collaborative" Series
A Dirge for Sabis (1989) with Leslie Fish
Wizard Spawn (1989) with Nancy Asire
Reap the Whirlwind (1989) with Mercedes Lackey
A highly regarded fantasy trilogy (also not read).
Russian Trilogy
Rusalka (1989)
Chernevog (1990)
Yvgenie (1991)
Two highly regarded fantasy singletons (also not read).
The Goblin Mirror (1992)
Faery in Shadow (1993)
A small press collection that has nothing of substance not available elsewhere.
Glass and Amber (1987 C)
3. 1994-present
After what was really a significant lull in her (at least SF) career, she rebooted by returning to DAW and producing the successful and never-ending Foreigner books (some of the other books were still published by others). The Foreigner books are apparently tightly connected to each other but were intended to be separate from U/A - they may have been joined at some point - I don't know. (I read the first couple-three but then quit when she released the fourth, or something like that. They were okay but I didn't want to get involved in another open-ended Cherryh series.)
Foreigner Series
Foreigner (1994)
Invader (1995)
Inheritor (1996)
Precursor (1999)
Defender (2001)
Explorer (2002)
Destroyer (2005)
Pretender (2006)
Deliverer (2007)
Conspirator (2009)
Deceiver (2010)
Betrayer (2011)
Intruder (2012)
Protector (2013)
Peacemaker (2014)
All she's done in U/A is tack on two more Merchanter novels for Warner, similar in kind to, e.g., Rimrunners, but singletons at heart (Tripoint was excellent; Finity's End was not) until, after a dozen-year gap, doing Regenesis for DAW. I think that's a direct sequel to Cyteen. (It's in The Pile.)
U/A Part 3
Tripoint (1994)
Finity's End (1997)
Regenesis (2009)
A fantasy quintet.
Fortress Series
Fortress in the Eye of Time (1995)
Fortress of Eagles (1998)
Fortress of Owls (1999)
Fortress of Dragons (2000)
Fortress of Ice (2006)
A science fantasy duo (I think - maybe pure fantasy), apparently unconnected to U/A (but unread).
Finisterre Duo
Rider at the Gate (1995)
Cloud's Rider (1996)
A belated TV tie-in novel.
Lois & Clark (1996)
A series that, again, was intended to be separate from U/A (so I skipped it) but was apparently belatedly connected somehow. This was apparently supposed to be more than a duo but maybe wasn't very successful.
Gene Wars Duo
Hammerfall (2001)
Forge of Heaven (2004)
The definitive, comprehensive Cherryh short fiction collection.
The Collected Short Fiction of C. J. Cherryh (2004 C)
tl; dr
She wrote numerous Union/Alliance books that are mostly single within the universal backdrop and don't form a connected larger plot, though there are subsets within that universe of Chanur, Faded Sun, and even Morgaine books. Also, there are books, still loose, which focus more specifically on the Merchanter Alliance ships or Union worlds which are similarly single-like except Cyteen/Regenesis. Then she's also written the huge Foreigner series and small Hammerfall duo. For fantasy, none of the series of Ealdwood, Russian, or Fortress are related to anything else, as far as I know, and there are a few singletons. And then there are Merovingen Nights, Hell, and Sword of Knowledge "junk" series as well as the Lois & Clark tie. For her short fiction, you can get Sunfall/Visible Light or get the Collected Stories which includes those two and previously uncollected stories equal in length to either of the earlier collections.