Popular Space Opera Series
There are many long space opera series, many still going strong, often in the military SF sub-genre. Rather than gather each separately, I have tried to list the reading order of several popular series here in one place, along with providing a few comments.
Lois McMaster Bujold's Vorkosigan Series
Pros: Hugo & Nebula Award winning, good characterisation
Cons: Writing is variable in my opinion, despite all the awards
1. Falling Free, 1988 - Nebula Winner & Hugo Nominee
2. Shards of Honor, 1986
3. Barrayar, 1991 - Nebula Nominee & Hugo Winner
4. The Warrior's Apprentice, 1986
5. The Mountains of Mourning, 1995 - novella
6. The Vor Game, 1990 - Hugo Winner
7. Cetaganda, 1996
8. Ethan of Athos, 1986
9. Labyrinth, 1989 - novella
10. The Borders of Infinity, 1989 - novella
11. Brothers in Arms, 1989
12. Mirror Dance, 1994 - Hugo Winner
13. Memory, 1996 - Nebula & Hugo Nominee
14. Komarr, 1999
15. A Civil Campaign, 1999 - Nebula & Hugo Nominee
16. Diplomatic Immunity, 2003 - Nebula Nominee
17. Captain Vorpatril's Alliance, 2012 - Hugo Nominee
18. Cryoburn, 2010 - Hugo Nominee
19. Gentleman Jole and the Red Queen, 2016
Elizabeth Moon's Space Opera Series
Pros: Highly readable and intriguing ideas
Cons: A touch derivative perhaps
Serrano Series
1. Hunting Party, 1993
2. Sporting Chance, 1994
3. Winning Colors, 1995
4. Once a Hero, 1997
5. Rules of Engagement, 1998
6. Change of Command, 1999
7. Against the Odds, 2000
Vatta's War Series
1. Trading in Danger, 2003
2. Marque and Reprisal, 2004 (Moving Target in UK)
3. Engaging the Enemy, 2006
4. Command Decision, 2007
5. Victory Conditions, 2008
David Weber's Honor Harrington Novels
Pros: Great space battles
Cons: Perfect lead character can be annoying;
Some books too long and need editing
1. On Basilisk Station, 1993
2. The Honor of the Queen, 1993
3. The Short Victorious War, 1994
4. Field of Dishonor, 1994
5. Flag in Exile, 1995
6. Honor Among Enemies, 1996
7. In Enemy Hands, 1997
8. Echoes of Honor, 1998
9. Ashes of Victory, 2000
10. War of Honor, 2002
11. At All Costs, 2005
12. Mission of Honor, 2010
13. A Rising Thunder, 2012
14. Uncompromising Honor, 2018
David Drake's RCN Novels
Pros: Entertaining, engaging characters, Drake is a combat veteran
Cons: The writing is a little workman-like perhaps
1. With the Lightnings, 1998
2. Lt. Leary, Commanding, 2000
3. The Far Side of the Stars, 2003
4. The Way to Glory, 2005
5. Some Golden Harbor, 2006
6. When the Tide Rises, 2008
7. In the Stormy Red Sky, 2009
8. What Distant Deeps, 2010
9. The Road of Danger, 2012
10. The Sea Without a Shore, 2014
11. Death's Bright Day, 2016
12. Though Hell Should Bar the Way, 2018
13. To Clear Away the Shadows, 2019
Jack Campbell's Lost Fleet Novels
Pros: Nice concept, well written
Cons: Not all characters worked for me, but I've not
read enough to really judge
1. The Lost Fleet: Dauntless, 2006
2. The Lost Fleet: Fearless, 2007
3. The Lost Fleet: Courageous, 2007
4. The Lost Fleet: Valiant, 2008
5. The Lost Fleet: Relentless, 2009
6. The Lost Fleet: Victorious, 2010
7. Beyond the Frontier: Dreadnaught, 2011
8. Beyond the Frontier: Invincible, 2012
9. Beyond the Frontier: Guardian, 2013
10. Beyond the Frontier: Steadfast, 2014
11. Beyond the Frontier: Leviathan, 2015
12. The Lost Stars: Tarnished Knight, 2012
13. The Lost Stars: Perilous Shield, 2013
14. The Lost Stars: Imperfect Sword, 2014
15. The Lost Stars: Shattered Spear, 2016
16. The Genesis Fleet: Vanguard, 2017
17. The Genesis Fleet: Ascendant, 2018
18. The Genesis Fleet: Triumphant, 2019
Timothy Zahn's Cobra Novels
Not read, so cannot provide pros or cons,
except to say Zahn has written other good SF
1. Cobra, 1986
2. Cobra Strike, 1987
3. Cobra Bargain, 1988
4. Cobra Alliance - Cobra War Book 1, 2009
5. Cobra Guardian - Cobra War Book 2, 2011
6. Cobra Gamble - Cobra War Book 3, 2012
7. Cobra Slave - Cobra Rebellion Book 1, 2013
8. Cobra Outlaw - Cobra Rebellion Book 2, 2015
9. Cobra Traitor - Cobra Rebellion Book 3, 2018