Aside from saving money, there are a few things that can make you feel even better about a decision to dry on the line. Fresh scents from blowing in the wind and time spent in the sun hanging the garments are some of my favorite benefits. What I am not so keen on is stiff clothing and lint from dust and the tree that shades my line (it's the only place that I could put it).
Check out mom advice for some more tips and benefits to line-drying clothing. If you would like a more mathematical reason to put some clothes up on the line occasionally, check out Funny About money, where how much you save (roughly) by line drying can seem like just a little bit (at first). I think that it really depends on what you use. We do not use dryer sheets or special anything when we dried our clothes before our dryer broke. Someone who does use a lot of that could save more by line-drying overall because they'd not be able to use it. Make sense?
Even if you're not into putting up a clothesline, you can always get a clothes rack and some clothespins to air-dry items that you do not want damaged in the dryer. Cloth diapers are a big one for me. Sure they're softer after being dried, but it also wears down on the waterproof fibers. They're not super cheap up front, so I want them to last. Same with lightweight clothing that I won't need for a while. It can dry overnight, be ironed out if needed in the morning and saved from the dryer heat.
When we did have a dryer, the one thing that I would finish up to soften the fabrics was blue jeans. Those suckers get so stiff! But since I have read lately that half to 3/4 cup vinegar in the wash can keep them from getting stiff, I can do away with steam ironing jeans to get the stiffness out. Should save me a lot of time, especially because I hate ironing and have lots of denim!
For me, a few clothespins and drying rack are a great benefit to energy usage over a long term. A few dollars a year can seem insignificant until you keep adding years and dollars is a great benefit. :-}