Because of the time period, the finish is more than likely lacquer or a varithane and unless you can successfully color match, you'd be time and money ahead to think in terms of a complimentary opposing tone or a complete strip and refinish.

Have you tried restor-a-finish followed by their wax. These products work fabulously well. You could do the whole kitchen in one day. It MUST be well ventilated.
The way it works is by adding a teeny bit of color to the surface. The color. only gets absorbed where there is no finish anymore. So the results are perfect. BUT if you intend to refinish the cabinets it is a problem because those areas will still retain some of that added color when you strip the cabinet. So if you really aren't going to strip the cabinets this would be the way to go but if you're intending to strip and refinish in a year or two you might as well just do it now.

I also was going to suggest restore-a-finish. Check out FAQ below.

Here is a link that might be useful: FAQ on restore-a-finish

Can you post a picture? It might depend on how the maple has aged.

I had the same problem with clear coated oak cabinets in our previous house. I cleaned them well and sanded VERY lightly, then followed with a coat of clear. They looked fine.

If the maple has darkened with age, this approach might not work. Maybe you can find an inside surface or an inconspicuous spot to experiment with.

Thanks, Nosoccermom and Practigal. I may at some point want to refinish completely, so I don't think I would want to use that Restore product, but, I like the idea of using a wax, if I can get it to where I want it. Is there a wax product you could recommend?

Anna, Here are two photos. First one is the inside of the cabinet where you can see how light the maple is. The exterior of the cabinet has darkened significantly.

I like the idea of how you took care of the problem at your old house. Might be worth considering. Even if the newly lightly sanded finish would be lighter, I imagine it would age as well and catch up to the old surface?

I think the first place to start is to clean the exterior as well as I can. Some of the finish has worn off around the knobs on the most used cabinets and drawers too. I wonder if anyone can recommend the right product to do that, that will gently remove the dirt and not take off the finish?

Not the best photo with the reflection on it, but best I could do this time of day. You can see how much darker it is than the inside.

Restor-a-finish also sells a clear version but I'm not quite sure how it works. I understand that the company is quite responsive to questions, so you may want to contact them. The wax is excellent and may do the trick without any further chemical intervention.