Should I buy a GPS for hiking that I will be doing in Yellowstone, Zion, Bryce, Canyonlands and Arches National Parks, or, are the trails marked well enough to allow me to day hike?

Usually the trails are clearly marked or discernable at the popular national parks. Besides using maps and compasses, today lots of folks are buying GPS devices, not realizing that there's more to using a GPS than just the device. You will still need topo maps, a compass, and the knowledge to use them. The GPS just helps you to identify your position on a map. You now need to know how to translate that map position to your visual surroundings in order to take advantage of the position which the GPS gave you. Some GPS allow you to backtrack your steps, but you don't want to be watching a small screen on the GPS rather than the scenic lands you're hiking. One trick I use to help me know my way when hiking is to frequently turn around and look behind me. That way I'll be able to recognize landmarks when returning.

However, if you know how to navigate with a compass and a map, then you really don't need a GPS device. The Park Service has nice trail maps/brochures at the visitor centers at the entrances to the parks. Be sure to get these when you arrive. They identify trail heads and other key information about the day-hike routes.

I hope this helps! I'm not meaning to discourage the use of GPS, because they are a useful tool; but I wouldn't consider them necessary for day-hiking in the national parks. Besides, you don't plan on getting lost, do you?