Why is someone sending out files from my account pretending to be me?

calumEMCS wrote:

The email sender (pretending to be me) is no-reply @ dropbox.com How can this be? 

This is simple. It takes a few seconds to spoof an outgoing email address. That isn't the actual address its coming from that's just what the person has set the email as being. 

You can almost certainly do it yourself if you were so inclined. 

Sadly there really isn't anything Dropbox can do because it isn't them sending the emails, it is somebody trying to scam people using your details. 

My genuine concern however would be why you are being targeted - have you got a virus? Malware? Unsecure passwords? Network etc. 

I'd do a checkup of your personal setup and make sure its a secure password etc. as well as look for unknown devices here: https://help.dropbox.com/security/security-checkup