Multiple instances of a field, differently formatted - how? And if I wanted a particular field displayed on a node twice, but each instance built with a different formatter - what should I do?
Example: a term reference field - formatted as plain text at the top, and as a link - at the bottom of a page.
I would use Panels. You can add each field as many times as you want and pick a different formatter every time.


Install the Chaos tool suite (ctools) module, and Panels.
Enable the Page Manager and Panels.
Enable the node template 
Create a variant of type "Panel".
Pick a suitable layout.
Go to the "Selection rules" settings and add a "Node:type" setting so this is used for a single node type.
Add your fields and select your formatters.
Save


Using Panels requires a bit of understanding of the tools it provides. There are a few videos here.