I have a web service I\'m offering to users to tap into my applications database and get some info. Users have to register for an API key and provide that when making requests.
There are 2 parts to authenticating REST API calls. When a user registers with your service, you will typically assign a KEY identifying that user. Sometimes, this is enough. But this KEY can be shared, or stolen. In which case, your service will still consider the KEY to be valid. Now, in order to prevent key hijacks etc. you will also distribute a secret key. This key is never transported with the REST API request. This key is used to perform a one way hash of the API request, and create a signature (HMAC).
This signature, plus the API request (HTTP request in the form of URL) is then sent on to the API Server. The server performs the one way hash of the URL and compares with the signature using the private key of this user. If they match, it is "assumed" that the requester has access to the private key, and therefore the request is valid.
In order to avoid replay attacks, in addition to nonce (as suggested by the previous poster), you can also use hash chaining.