We go through a lot of herbs at home. And by go through, I mean reaching into the vegetable bin to find a putrid, liquified bag of something that used to be green. Oops!
When stored the right way (in a glass jar, covered with a plastic bag, in the refrigerator) cut herbs can last up to a week. Sometimes I do this. But usually there are too many containers of Dan's Dannon coffee yogurt or containers of odd condiments to also fit several jars of water in our fridge. So into the vegetable bin/death chamber they go. I've also heard that you can freeze fresh herbs, which I haven't tried yet.
Another way to use them up is in arrangements. Sometimes I tuck sprigs of herbs into bouquets, creating a fragrant filler. Or, when I buy a huge bunch of basil or mint for $2 at the farmers market with ambitious plans to make big batches of pesto that fall short, I'll just make an all-herb bouquet. It makes the house smell nice and makes me feel less guilty about not using the whole bunch.
Any fresh herb will work as filler, although the larger the leaf, the easier it is to work with. Basil, cilantro, mint, oregano, and sage are all good options. Just make sure you strip off any leaves below the waterline to prevent rotting. For herbs with woody stems like rosemary, lightly crush the ends of the stems to help them soak up more water. This is a good trick for thick, woody flower stems too, especially hydrangeas.