What are the assortment of medals that can be issued in the military and what are they awarded for?

Which country ?

If the US, what branch of the service ?

Don't know why I didn't mention that, probably would have helped haha, but the US navy is what I was referring to.

Try going to military.com... they should have pictures of them all and a description on how to earn them

It would really take a long response to answer such a question and you would not believe the variety of medals that a military person can receive. My son is a sergeant in the 82nd Airborne Division and even has jump wings from the government of Chile when he jumped with one of their teams. This site lists Navy medals:

Navy Medals and Ribbons