I just don't know how you can pick 25 greens from the range of things out there. I don't even know that I could pick 25 from my own body of work ... and my work wouldn't account for even 1% of the total number of great greens out there.
Heck, on Lost Dunes alone, there are a number of great ones that get no recognition because #4 is such a lightning rod:
The third green there is amazingly severe for a green where the difference from highest to lowest point is probably only two feet.
The seventh green is one of the coolest approach shots on the course, with the right wing falling away from play and encouraging you to use the ridge in the left-center to feed the ball in, with the same ridge also making for a great tight left hole location.
The twelfth green is pretty wild, too.
Yet, I would have to say my favorite of all of those is the eleventh, with its high right plateau and backboard.
And that's just Lost Dunes. White Bear Yacht Club has just as many, and I don't think anyone has mentioned it.
PS Thanks Tom Dunne for reminding me of the fifth green at Walton Heath. I had just about forgotten it over the years, but played there two years ago and just couldn't stop smiling after I saw that one again.