I always had the regular chairs you always see behind a desk. But a while ago I bought a Skruvsta from Ikea. From all the computer chairs they had standing around there, this was a really good one.
http://flickr.com/search/?q=skruvsta&w=all&s=int
http://www.ikea.com/us/en/catalog/products/80121649
It's very relaxed and has good support for your back. On the pictures it seems like your arms will slide off, but they don't; it's all good. Perfect for desk work, and it has a lever you can pull out so it'll lean back all the way; very good for watching tv, reading a book with your feet on the desk, etc.
Oh yeah, and it's light and for $139.00 not that expensive for its kind.
Give it a try!