The ribbon signifies award of the medal. If you were given a medal, you got a corresponding ribbon. Wear of medals is generally restricted to formal occasions. Ribbons are required wear on Class "A" uniforms, optional on semi-dress (shirt sleeve blues in the USAF) and never worn on utilities. Medals are worn on the Class "A" on formal occasions.
The ribbons that don't have a corresponding medal are those that are awarded automatically, or to a group of people such as outstanding unit citations, etc. Most of what is seen over the left breast pocket are the latter type ribbons. "Fruit salad" is the common term for the left chest full of ribbons.
I don't know why you wouldn't want to if you were awarded some medals....BUT you can wear your service uniform without any ribbons.