Will applying a tag to a contact that already has that same tag trigger the tag goal?

We have about 40 different pieces of content that can be downloaded from our site. I’m trying to apply the same tag in each campaign so I can get stats on total downloads. If someone has already had the tag applied and they download something else later, will the tag goal be achieved or ignored because the contact already has the tag.

If the person already has the tag, the tag goal will not fire.
You should set up 2 types of tags — a System (or Trigger) tag and a Profile tag.

You can add the System tag when the download occurs to put them into whatever sequence you want to trigger.
In that sequence, immediately remove the System tag and then add the Profile tag. This will allow you to keep the Profile tag on the contact but allow the System tag to trigger each time they download.