Lots. Because many upstream projects don't have their build system set up to work within a distribution (to get dependencies form the system and to install to standard places). All distros must patch things to get them to work.

Well, there are big differences in how aggressively things are patched. Arch Linux makes a point to strictly minimize patches and avoid them entirely whenever possible. That's a good thing, because otherwise, nonsense like the Xscreensaver situation ensues, where the original developers aggressively reject distro packages for mutilating their work and/or forcing old and buggy versions on unsuspecting users.