For the most part, Dropbox's two-factor authentication is only used when you login to the service's website from an unknown machine. You will only have to authorize Dropbox desktop apps at installation or after setting up two-factor authentication.
The company's mobile apps require two-factor authentication every time you sign out of the app, which might happen if your tablet or smartphone powers down or reboots.
Check out PCWorld's hands on with Dropbox two-step verification for a more detailed walkthrough of the process.
Facebook doesn't use Google Authenticator for its two-factor authorization, which it calls Login Approvals. Instead, you receive login codes via SMS or you generate them with the Facebook mobile app.
To get started login to Facebook and go to the Security tab. Find the heading that says Login Approvals and click Edit on the far right side of the screen. Facebook will then send a security code to your smartphone via SMS to get started with the feature.
If you are ever in an area without cell reception, you can still use Facebook's login approvals via the Facebook mobile app for Android and iOS by opening the left-hand navigation bar and selecting Code Generator under Settings.
Facebook's login approvals work with almost anything that connects to your Facebook account including third-party mobile apps with Facebook logins and the company's own apps.
What other services need this?
Now you're all set-up with two-factor authentication for several of the major online services. But there are a ton of services out there also supporting two-factor authentication including major Web hosts such as Dreamhost, Blizzard Entertainment's Battle.net, and LastPass.
If you're concerned about security, enabling two-factor authentication on these accounts will go a long way to making your online life more secure.