What's the greatest pirate themed movie of all time?

The Curse of the Black Pearl, and it's not particularly close.

It's a movie that I saw, enjoyed, and mostly wrote off when it came out. But here we are 20+ years later and I'm still rewatching it every few years. It is still just over-the-top over-acted ridiculous silly fun.

Very well-paced and quotable. Main characters (Knightley and Bloom) were unremarkable, but the side characters (Depp and especially Rush) put in excellent performances into very silly roles.

It's not The Godfather, but it's not trying to be. It is pretty perfect at everything it did try to be.
I feel like the second and third movies are underrated. Perhaps not as tightly scripted as the first, but if you watch them back to back it's a fun ride.

And Keith Richards plays Jack Sparrow's dad in the third film.
- Agreed. I don't really like the second, but the third is a very good ending for a trilogy that had no right to be as good as it is. I especially love how all the characters have these different changing motivations and how that shapes the plot.
  
  The first is just perfect, though, not even close
I'm with you, too. It was super good in theaters (get off my lawn).

Does The Goonies count?

First I thought of

Treasure Planet

Muppet Treasure Island

Princess Bride

Meh, great movie, and yes there's pirates, but I wouldn't consider it pirate-themed personally
- I mean, the main character, Westley, is literally The Dread Pirate Roberts. And there's swashbuckling, sailing, and a ragtag group of outlaws who come together despite all odds to fight the crown and take it's treasure (Buttercup).
  
  That's a pirate movie.
- Yeah, I suppose it's not the most heavily themed pirate movie

Muppet Treasure Island

Hook 👏👏👏

Don't try to stop me smee, try to stop me smee

I don't know if it's the greatest, but Ice Pirates is too often overlooked.

This fucking movie has stuck with me for decades. It is so stupid and hilarious.

This flag means death is killing it for a show

Cuthroat Island

It's an underrated movie, Gena Davis knocks it out of the park!

Pirates (2005)

Also Yellowbeard

Pirates II: Stagnetti's Revenge is unironically a really fun watch. Evan Stone is hilarious in it.
- They made an R-rated cut with the sex scenes edited out and it's surprisingly watchable (in a low budget campy way)

Disney's 1950 Treasure Island - yes Depp's Jack Sparrow is great, but the pirate performance par excellence is Robert Newton's Long John Silver, imo

[off topic?]

TV show 'Black Sails' has it all. It starts with a great pirate raid and has everything you want. Buried treasure, hidden islands, scheming ladies, backstabbing, and more. Great writing and superb acting with incredible action sequences.