There is a project called Twurl - an OAuth-enabled curl for the Twitter API:
Twurl is like curl, but tailored specifically for the Twitter API. It
knows how to grant an access token to a client application for a
specified user and then sign all requests with that access token.
It also provides other development and debugging conveniences such as
defining aliases for common requests, as well as support for multiple
access tokens to easily switch between different client applications
and Twitter accounts.
Instead of this from the question:
curl -d status="Your Message Here" https://twitter.com/statuses/update.xml
you use something like this:
twurl -d status="Your Message Here" /1.1/statuses/update.json
after you authorize yourself first as explained in the readme.
(note that you don't have to use the protocol and hostname in the URL as you would with curl)
This program was originally written by Marcel Molina who worked at Twitter at that time and it is now an official Twitter project on GitHub.
Many people are asking specifically how to use curl to use the Twitter API and twurl is probably the closest to curl as you can get today.