As tweakt said, Amazon S3 is a good model to work with. Their request signatures do have some features (such as incorporating a timestamp) that help guard against both accidental and malicious request replaying.
The nice thing about HTTP Basic is that virtually all HTTP libraries support it. You will, of course, need to require SSL in this case because sending plaintext passwords over the net is almost universally a bad thing. Basic is preferable to Digest when using SSL because even if the caller already knows that credentials are required, Digest requires an extra roundtrip to exchange the nonce value. With Basic, the callers simply sends the credentials the first time.
Once the identity of the client is established, authorization is really just an implementation problem. However, you could delegate the authorization to some other component with an existing authorization model. Again the nice thing about Basic here is your server ends up with a plaintext copy of the client’s password that you can simply pass on to another component within your infrastructure as needed.