Neville

For national parks I guess it would largely depend on what you're looking for. There's a lot of good ones for solitude and others that represent a chapter in our history. Good ones for hiking/backpacking and others where spectacular sights can be seen from the car. These are the ones I like the most:

1) Isle Royale National Park - My personal favorite for backpacking.
2) Yellowstone National Park - One of the most diverse.
3) Big Bend National Park - Good for solitude and desert hiking.
4) Bryce Canyon National Park - Great scenery.
5) Mesa Verde National Park - Lots of ancient history there.

State Parks:
1) Big Bend Ranch State Park - Just like it's neighbor Big Bend NP.
2) Lost Maples State Natural Area - The best overnight backpacking trip in the park system, especially in the fall.
3) Devil's River State Natural Area - The best for solitude.
4) Caprock Canyons State Park - Excellent dayhiking.
5) Palo Duro Canyon State Park - Good for dayhiking as well.