We once did have a ring around the Earth. When the proto-planet Theia crashed into the Earth, a huge amount of material was thrown up into orbit, forming a ring. Eventually, however, it coalesced into our Moon. But imagine if it hadn't. What would our view from Earth be like?
If we had rings in the same proportion to our planet that Saturn's are to it, it is pretty easy to figure out what they would like from different places on the earth. From the equator the rings would look like a bright line arching from horizon to horizon:
If we travel just a little further north to Guatamala, the rings begin to spread across the sky.
Moving to somewhere in Polynesia on the Tropic of Capricorn, a 180° panorama gives an idea of what a magnificent sight the rings would be. The dark, oval-shaped break in the middle of the ring is the earth's shadow.
From Washington, DC (at 38° latitude), the rings begin to sink below the horizon, though they would still be an awe-inspiring sight as they dominate the sky both day and night.
At the Arctic Circle, the rings barely reach above the horizon. Seen here from Nome, Alaska, the brilliant rings illuminate the barren landscape scarcely more than a full moon would. Unlike the sun or moon, however, the rings neither rise nor set...they are always visible, day or night, always in exactly the same place.