For the most part, you can't ride on an Interstate highway. There are some exceptions where the Interstate is the only road around. Think the Nevada desert.

There's even a few exceptions for crossing over rivers on Interstates. Technically you can cross over the JB Bridge on I-255 south of St. Louis. However you can't ride on the approaches. Therefore you need to walk your bike up the grass hill to the bridge; ride across; then dismount and walk off the grass side of the bridge.

There are some states that have different laws for limited access highways. These highways are often almost identical to interstates.

However most roads in the US can be legally ridden on by bicycles. However legally and sensibly can be two different things. I've ridden on Route 66 quite a bit. There's some places where it's fine and others where it's best to take a side road. In fact most tourers tend to take scenic side roads.