Qt is a cross platform ui toolkit so will conform to the OS style accordingly. Unsurprising then that Qt will use the Windows recommended button height when on a windows platform which is 21 pixels border to border inclusive, on Vista and Windows 7, as per the MS UX guidelines. On Mac OS X then the standard button height is also around the same height and I believe if you resize a pushbutton up to 23 pixels, it changes from a round ended push button to a square ended button. I think the Aqua default button height is 20 pixels.
However, if you look Qt's example stylesheets that are distributed with Qt by default, then themes like PageFold use a height of 22 pixels, and Plastique 23 pixels, and CleanLooks a huge 33 pixels.
Now personally, if I repeatedly draw out the size of a button that 'seems a nice and comfortable size to use' (for a text push button on a desktop application), then I almost invariably end up with something around 90x26. A height of 26 tends to be what I use when designing an interface from scratch (although some applications I have designed have looked better with buttons up to 35 pixels in height). At 26 pixels, the appearance seems nice on the eye and it's a little less fiddly to use whilst not looking completely out of place or too chunky.
But I feel bad that I disagree with Microsoft and Apple, after all they've probably spent rather more time and money coming up with a height of 21 than I have coming up with 26. On the other hand I like to design interfaces that do not have huge amounts of functionality crammed into a space and therefore if I use buttons with a height of 21 pixels then the buttons look all lost and alone, so it can be a matter of how it fits in with the rest of the design, and how much control you have over the whole application - since it's also important to be consistent. I think context is definitely going to be a factor in the ideal button size in a given situation.
I also just noticed that when I upload an image here on SE, the upload/cancel buttons are 91x26, so at least I know I'm not alone in liking this size :-)
So here's my ideal button size: