I have an external hard drive that I would like others to be able to access what is on it but not the ability to delete or edit anything on it. Ideally if a user tries to write to the drive or delete something on it the drive would ask for a password.
Does any software like this exist?
This might be possible, but the usual way to make this work is that you give some users read-only access and others read-write access. So the 'password' would be the user account and the way they are accessing the drive. Also, depending on the operating system (it's true at least for Mac OSX), you CAN allow read-only access that then prompts for an admin [computer user] password if you are doing something not allowed.
There are also security software packages that will allow you to password protect data and some might allow reading but not writing-- this exists, for example, for thumb drives. Search a bit and you might find something, though I'm not sure if it does exist in the way that you want.