I want to delete Dropbox from my work computer.
Can't I simply remove/uninstall the Dropbox program from this computer in order to remove the computer from my Dropbox account? Or, will uninstalling the program from my work computer somehow adversely affect all of my files on Dropbox.com by deleting them along with this computer as well as from my laptop and cell phone? I do have my laptop and cell phone synced with my Dropbox account.
You should be just fine. Uninstall Dropbox, then delete the Dropbox folder and its contents. (Not the other way around.) That should not affect your files saved in Dropbox.
To be safer, right-click on the Dropbox app in your Notification Area, choose the gear, and then "Exit from Dropbox" before you proceed. That will ensure there's not synchronization going on at the time.
To be extra safe, go to your account on Dropbox and go over to the Security tab. There you'll find a list of devices that are connected to your account. Click the × on the right side and confirm to disconnect the device from your account.
