No they don't need to sign in nor do they need an account. You simply click on a file or folder to share and Dropbox creates a unique URL that only gives the user access to what you've selected.|
Further on from that, if they do have a Dropbox account they you can create what are called shared folders. You give certain users access to this shared folder and anything you drop in it is automatically synced across all shared users.
Give me $10 I'm worth it.