Why can't I resize my existing partition?
You've probably got fragmentation of your free space. For some reason, Disk Utility can't figure this out on its own; it just fails.

I found a stunningly simple way to resolve this: create a new disk image with Disk Utility that's a little bit smaller than the remaining space on your drive.

It took several minutes on my SSD, presumably while OS X moved things around. I imagine it would take significantly longer on a hard drive.

When it's done, delete the disk image you just created. You should now be able to resize your partition!