You can change your password from the account settings page on the Dropbox website. You only need to make the change once and when you do, it will automatically apply to any computers or mobile devices linked to your account.
When using the Dropbox desktop application, you only need your password when you first install the Dropbox desktop application or whenever you link or relink your computer to your Dropbox account. Control all access to your Dropbox account via the Security tab of your account settings on the Dropbox website.
Enter your email address at the forgot password page on the Dropbox website. An email will be sent with a link you can use to reset your password.
If you have changed your password, but are concerned about unauthorized access from a computer linked to your Dropbox account, you might consider unlinking the computer from the Dropbox website.