What HTTP request headers are important/commonly used?

I'm writing a web server, and I'd like to know what HTTP request headers (sent by the client) are the most common and thus that I should focus on impleme开发者_如何学Cnting.

Right now, I only support Accept and Host.

Not sure on your scope but since you are interested in serving web browsers, you should have a look into the RFC (HTTP 1.1)
Read about what the server MUST process

The Cookie header might be a good idea, as would the Content-Length header; without Content-Length you won't be able to handle POST and PUT requests properly.