Unlinking your Facebook or Twitter account can be done by visiting your Account Settings. Once there, you can click the unlink button next to the name associated with your Facebook or Twitter login.
Connecting your Twitter or Facebook account to your Dropbox account is completely optional. To link or unlink your account, go to your Dropbox account settings.
For more information on adding or removing apps, see Facebook's Help Center.
Once you disconnect from Facebook and/or Twitter, you'll no longer be able to send messages or access your friends from the Shared folder dialog or through the Referral page. You'll also no longer be able to use Dropbox to share files with Facebook groups you belong to.
If you received free space by connecting your Twitter and Facebook accounts through the Get Extra Space Free page, you will keep that space even if you unlink your accounts. You won't be eligible for more free space should you reconnect your accounts.