A business card size version of the logo we made for our comic Li'L Nyet.
There's still room for other information.
You have a great comic logo, but when you designed the site, you made a few mistakes that made it unusable. Don't panic.
The most common errors are overlapping it with other art and saving it as one file, putting text on it such as navigation cues, and making it in Flash and snaking it around things so that a screen grab can't get at it.
A good logo has your comic name, art that tells about the comic, possibly the creator's names, possibly a slogan, possibly characters in a milieu and nothing else. Ideally, it is an irregular shape, both for getting attention and for distinguishing it from the tired old banner look.
The best cure is prevention, but if you make a mistake, Photoshop can cure most errors. If you don't know how to use it, buddy up to someone who does. I've been known to fix stuff in exchange for small courtesies, such as planting my links on your sites and strong-arming friends to do the same.
I maintain the logo gallery at Psychedelic Tree House, and I'd love to have a great logo listed for every web comic. Being listed at PTH is like having a banner ad in a museum. It helps you get traffic. It gives you instant art for DIY t-shirts, letterhead, business card and other stuff. If you're in school or a relaxed workplace, you should wear your logo t-shirts often. Heck, make variations and wear them every day.
Looking through the galleries at PTH is also very instructive.
As I've written recently, you can make very decent tan or white t-shirts with Avery transfers and an iron. (Avoid the dark ones.) Why not have a logo t-shirt to wear to your next social event? Make sure to bring business cards with your site URL so people can look you up later.