So I've got an outside hose connection where I can't completely shut off the water. Even with the handle cranked tight, water still is coming out--and not just a small drip either, but at a reasonable volume.

How can I stop this and get the valve shut?

Thanks,
Rob

This may not look like your hose bib,(see image) but the insides are all the same. Shut the water off to the hose bib and unscrew the large bonnet packing nut. Back the stem and washer assembly out counterclockwise and replace the washer. Check the seat for nicks and rough edges. If you find any the hose bib must be replaced or it will just tear up the new washer. Good luck, Tom