Admittedly there are series by other authors which I have not read, like Elizabeth Moon and C. J Cherryh so I must admit that my dataset is incomplete. But considering the Hugo Awards that Bujold has won I think I can be excused on that score.
Strictly speaking the series starts with Shards of Honor where the eventual parents of Miles Vorkosigan meet. The last book in series, so far, is Diplomatic Immunity, which is the first story after Miles' marriage. Off hand I don't know of any other series that covers a single character's life like this. In many ways it is most similar to David Weber's Honor Harrington series. But Honor is on some medical treatment called PROLONG, like everyone in her culture, and her life is rather of stretched out, and there is a kind of sameness that extends through Weber's work. Like things are constantly happening around her but no one is really changing.
The entire series has been reviewed by Russ Allbery and he uses a ranking system from 1 to 10 so I am going to use the same method.
Mr Allbery considers Shards of Honor to be the worst of the series and gives it a 4. I consider Warrior's Apprentice to be the worst and rank it at 5. Warrior's Apprentice is not the first in the timeline of the stories but it was one of her first books. She admits that it was submitted and rejected 4 times. Fortunately things got MUCH better. But although WA is not nearly the best it is one of the most important. Many major characters that are used in later books are introduced there. This book cannot be skipped. A nice position for a weak story. LOL
Mr Allerby and I agree that Komarr and A Civil Campaign are the best books in the series and we both rank them at 9.
Falling Free is part of the Vorkosigan universe but not really of the Vorkosigan series of stories since it precedes Miles' birth by about 200 years. It could be important to read for a couple of other reasons though. It introduces a "species" of genetically engineered humans who pop up in later stories, especially Diplomatic Immunity. It also presents a perspective on SCIENCE which a lot of so called SCIENCE FICTION books no longer do. Genetic engineering is an issue that the human race has to confront NOW! There may not be much radical engineering of humans soon but we do have TERMINATOR SEEDS which are of economic significance. Bujold's father was an engineer, as is one of her brothers. I am inclined to wonder how much the Leo Graf and Professor Vorthy's characters are like her father. Or her idealized father?
Bujold creates characters better and more interesting than just about anybody and puts them in fascinating and thought provoking situations. But most reviews concentrate on the characters and ignore the science that she puts into her books and the characters that do the science. Barrayar is the book that got me hooked on the series and it is the Vagaan character that is ultimately responsible for Mile's existence. Bujold created one scene where Cordelia first meets Vagaan which spoke volumes about the thinking of tech people but which the mundanes don't get. In Civil Campaign it is Enrique who is the sci/tech guy and source of much comic relief.
We live in a Geek driven world but the normals pretend they are not important. But the lives of the normals are affected by the products of the geeks. There are still thousands of nuclear weapons in this world that are products of some geeks at Los Alamos. This global warming business is being argued about though most of the geeks claim they agree. So the quality of life of the 21st century may be the result of not listening to the geeks.
But overall Komarr is my favorite of the Bujold series. This story involves the discovery of some NEW PHYSICS involving the imaginary physics that Bujold created. The behavior of Dr. Riva, the first female geek in a Bujold story, is fascinating in unraveling the core of the mystery of the tale. I have not seen a single review discussing this aspect as it relates to scientific investigation in the real world. For many it is just irrelevant background to justify Miles meeting Ekaterine. We need SCIENCE to make REAL SCIENCE FICTION and REAL SCIENCE has been making real life more and more UNREAL. Most of the stuff out there that gets called science fiction AIN'T. We need more real SF to get us in touch.
So here is my ranking for the entire Vorkosigan series:
Falling Free 7/10
Shards of Honor 6/10
The Warrior's Apprentice 5/10
The Vor Game 7/10
Brothers in Arms 7/10
Mirror Dance 8/10
A Civil Campaign 9/10
Diplomatic Immunity 8/10
Captain Vorpatril's Alliance 8/10
Captain Vorpatril's Alliance is a comedy like A Civil Campaign but the central character is Ivan Vorpatril, a supporting character, in many other stories about Miles. Miles just makes a cameo appearance as part of the humor.
If starting off consider getting Cordelia's Honor. It is an omnibus containing Shards of Honor and Barrayar.
The Vorkosigan series is now free and legal here: