If we go on vacation in the fall during the off-season, should we book hotels ahead of time?

It depends on where you're going. You'd be surprised at the number of people who travel in the fall. If you're going to any of the "leaf peeping" areas, hotels may be sold out. It also gets exhausting to go to hotel after hotel looking for a room. If I were you, I'd reserve the room the day before or the day you need it, so that you know you have a room waiting for you.

Two things:

1. MANY websites have both a non-refundable and cancel pithing 24-hours options. Sometimes those options mean the room is more expensive.

2.  If you are ok with running the slight risk that you might not get a room or the type of room/bed you want, then don't book ahead.  

3.  As Gypsyfish noted, you can book ahead the day before our sometimes the same day via a website -- or call the places you want to stay.  

I always book online ahead of time. If something comes up the prices jump quickly. Like all we have left is the honey moon suite at triple the price.

I have NEVER had a case where a non-refundable online booking was the same as walk-in price. I find that if non-refundable booking is 20% cheaper. Otherwise a reservation can be cancelled up until the day before. So if you don't go, and cancel it's no problem. But you do have to read the fine print and make sure on each booking if it's prepay, non-refundable or not.

i would call if you want to make sure you have a room

You should assume that the people working the front desk do not have the authority to give you a discounted price if you just walk in. What I do is book the room on my smartphone when I'm ready to stop for the night. I never book rooms in advance when driving.