I prefer to build Qt from source. I have been trying to build Qt 4.8.5 on Mac OS X 10.9 (Mavericks). I managed in the end, but it took a few tweaks. Online information about how to do this was fragmentary, so I am documenting it here in case it is useful to someone else.
1. Webkit doesn’t build. I don’t need it so I disabled it using configure option:
-no-webkit
2. The corewlan plugin doesn’t build. I don’t need it (I think, I’ve never heard of it before) so I disabled it using this fix from stackoverflow.
3. The TIFF image format plugin doesn’t build. I don’t need it so I disabled it using configure option:
-no-libtiff
My final configure command was:
./configure -nomake demos -nomake examples -debug-and-release -no-multimedia -no-audio-backend -no-phonon -no-phonon-backend -no-gif -no-openssl -no-webkit -no-libtiff
There will be lots of warnings that Qt 4.8.5 isn’t compatible with Mac OS X 10.9. But you can ignore these (or comment out the warning in the appropriate Qt header file).
I have done some brief experiments and it seems to work ok. Hopefully there will be a Qt 4.8.6 that fixes these issues. Note that you also need to make some tweaks to your application code. See:
** UPDATE April-2014 **
Qt 4.8.6 has been released. This appears to build fine on Mac OS X 10.9.

The text isn’t centre aligned. It doesn’t look like much of an issue out of context. But it looks wrong when you look at a whole UI. The good news is that there is a simple fix:
Much better! There are some console warnings: