Since there are no posts on this I decided to start one. This is for a 67 Parisienne with the standard AM radio, no factory A/C or tape deck.
1. OPTIONAL: remove glove compartment door and left hinge that stops door at horizontal position. Removing door will make the light stay on but also gives you more space to work.
2. From glove compartment remove 2 right screws, then from the top the 2 towards the right and the one all the way on the left. No need to remove the hinges where the compartment door closes.
3. At this point let the box slide back and down (if you have a tissue dispenser or anything else underneath it will be in the way.)
4. Now on the left you can see the 5/16" hex screw holding the radio in place. Take it out.
5. Remove volume knob, spring, bezel, tuning knob & bezel (careful, there's a small spacer between the two that can easily fall out) Don't remove nuts yet.
6. Unplug wire harness from below / behind radio as well as antenna lead
7. Back to the front ... remove nuts holding radio through volume / tuning control. At this point the radio will loosen.
8. As the radio drops there is another harness in the back going to the speakers. You can unplug it now.
It would have been nice for GM to leave a small hole on the left of the glove box to access the radio's hex screw. I decided to carefully make one myself in case I ever need to remove the radio again.