1. Kirk: Partly because he was my first (and there are no heroes like childhood heroes), partly because of Shatner's charisma in the role, partly because of the unfair stereotyping the character gets (see Kelvin Kirk) when he's really a complex character, partly because of his cleverness/determination/not believing in no-win scenarios/cheating death/Horatio Hornblower style heroism
2. Picard: I love Picard through 90 - 95 % of TNG and Patrick Stewart is obviously great in the role, but when the writers screwed him up they REALLY screwed him up (Homeward, his asking why Crusher saved the people in cryo in Neutral Zone): stuff that even as a kid watching left a very very bad taste in my mouth.
3. Sisko: Brooks is fun, it was great to see a single parent captain, and Sisko was tough. There's an argument to be made that he was guilty of a war crime or two, but I think they did an excellent job of bringing the viewer along his journey with him regarding his bringing the Romulans into the war (not so much the time he gassed a planet...). As some one who is adopted though I was always appalled by his (off screen???) decision in Cardassians.
4. Pike: He was interesting in The Cage, tragic in Menagerie and easily one of the best things about Discovery season 2. If they keep doing as well with the character in Strange New Worlds he may even go up on my list.
5. Freeman: She's often ridiculous but that's what you get for being the captain in a comedy. I was super impressed by her quick thinking in the season one finale though, not getting destroyed in the same way as the ship they'd come to rescue thanks to a lightning quick realization.
6. Burnham: The character has issues, mostly extensions of the issues with the show she's in, but I can't fault many of her calls since she became captain this season.
7. Kelvin Kirk: I like Pine, but this is (at least until Beyond) what all too many people who don't watch TOS think Kirk is.
8. Janeway: I have to disagree with the poster up the thread a bit who says being inconsistently written doesn't make her a bad captain: it absolutely does. Imagine some one that inconsistent in charge of something in real life. When she was good she could be very good, unfortunately that was all too infrequent.
9. Rios: We've seen very little of his captaining, but his backstory is (unlike so much in Picard season one) interesting to me.
10. Archer: This was understandable to a degree given he was chronologically the first human deep space captain, but near Janeway level uneven writing really exacerbated this. A waste of Backula.
11. Dal: Naturally: he's a punk kid, that's the point at this stage.
I regret that we never really got to see enough for me to rank Georgiou (prime), Lorca (prime), Saru (who I feel was great at the end of season 2 but sabotaged by the writers in season 3 to make way for Burnham), Spock, Sulu, April, Harriman or Garret.
Outside of "canon" I also like Calhoun (New Frontier), Martinez (Shield of Tomorrow) and Sul (Clear Skies). Also, though I've not seen much of him, the captain of the Enterprise F in Star Trek Online seems interesting.