The same issue is encountered by Twitter application developers. There are many, many Twitter applications out there - desktop applications, browser plugins, mobile apps and so on. In order to post from your account they obviously need to be "logged in" as you. One way of doing this is giving them your username and password (Basic Authentication) - and if you're testing out some of the many existing applications, more than a handful of developers now potentially have access to your Twitter account. This may not be the most high-security target in the world, but it illustrates the point.
The current answer to this is OAuth. Wikipedia's definition of OAuth is "an open protocol that allows users to share their private resources (e.g. photos, videos, contact lists) stored on one site with another site without having to hand out their username and password". The following diagrams serve to illustrate the difference between Basic and OAuth Authentication.

Obviously Step 1 in Basic Authentication and Steps 1-5 in OAuth Authentication only need to happen once. Furthermore, we can derive a number of advantages from the use of OAuth:
- No application ever has access to your password, so if you use the same password across different sites your identity is not compromised.
- The server can revoke access to any application at any time by removing its authorisation token from its database - useful in case the application is ever found to be doing anything non-professional.
- The user can see an entire list of applications that have access to their account, and what privileges they have. They can also revoke access at the click of a button.
- Changing the password does not prevent these applications from functioning.
Currently in development is the OAuth 2.0 specification, which focuses more on specific authorisation flows for various hardware devices - you can read the draft specification here.
Update: a recent episode of the Security Now! podcast went into OAuth in greater depth than I have here. If you're interested in the very technical aspects of it, along with the potential security vulnerability, you can read the transcript of the show or listen to the audio.