We're looking for recommendations on tour companies for North American parks. We would like to tour Mt Rushmore, Yellowstone, etc

What kind of tours? A full bus/van tour or day tours?
This is a great company for Yellowstone and the Grand Tetons -
http://www.brushbucktours.com/

My advice would be to do it on your own and not go with a tour company.

A lot of companies offer tours, both mainstream and luxury. Austin Adventures is a good company, but they are expensive and provide a certain level of luxury. But mainstream companies like Globus and Trafalgar also offer group bus tours of the national parks. Many parks have their own foundations that arrange guided trips in the parks. These kinds of group tours aren't really my thing, so I don't really have any first-hand knowledge, but I know that Austin is a reliable company, which is why I've mentioned them.

If you don't mind driving yourself, you can do this much much more cheaply by just renting a car and driving.

I would think about what you want to see and do in each park. Are you interested in short hikes? Long ones? Viewing wildlife and natural beauty as well as "sights"?

Tours tend not to spend much time in each park - so be sure whichever you look at spends enough time in the parks to see/do what you want.

The other option is to go to the parks and sign up for the ranger led programs. No extra cost, some involve hiking, others are demonstrations or explanations of history, geology, flora, fauna, etc. from various points in the parks.

We've always gone on our own and occasionally done ranger programs. We do have friends who have taken and enjoyed trips with various tour people.

The program that used to be Elderhostel and is now called Road Scholar was used several times by one couple who really enjoyed the educational bent of their trips.

We used Brushbuck tours as recommended in Starrs post.....wonderful....we did a full day upper loop tour with them, looking for wolves, grizzlies and moose and saw all of them with Bud (lovely lunch and snacks included). We drove the lower loop ourselves stopping at the geysers and mud pools easily doable with guide books and maps. We also took a twilight wildlife tour of the Grand Tetons with them (Clint), saw loads of wildlife and really cool birds plus a very close encounter with two bull moose that I will never forget...I would recommend a tour anytime, yes it's more expensive but IMO worth it especially if you are time limited and have a wish list of things you want to see (not guaranteed of course but they seemed to have the knack of being in the right place at the right time). You also have a commentary of the parks history which for Yellowstone is mind blowing!