The Finder Toolbar
The Mac OS X Finder has an interesting toolbar. blech will happily rant about it for hours, and I agree with him, toolbars do not belong on Finder windows. Or at least, not in the icon view Finder windows, and neither of us like the Browse view at all. But that's missing the point. I'm convinced the toolbar on Finder windows is a vestigal shelf, although I can't find anything on the web that backs this up, and I've never used NeXTStep, where the shelf was originally seen. You can drag things onto it from finder windows, and they'll stay there and you can run / open them by clicking on them.
The way it fails in this is that you can't drag files off the toolbar into another folder and move the original - dragging things off removes them from the toolbar. Arguably better from a least-surprise point of view, but it removes one of the nicest things about the shelf, it's use as a scratch area. Oooh, thought, this is exactly how the right hand side of the dock behaves, except you can't drag apps onto the right hand side of the dock.
Oh, and there aren't any tooltips, so if you have 'icons only' toolbars, you can't tell where things point. That's annoying.