We've always wanted to visit Washington, DC. Our main interest would be to visit the Smithsonian museums & various Memorials, etc.
Although it seems one never has enough time to "see it all", what would be a good amount of time to plan for? 7-10 days? Also, what time of year would be the best? We were thinking perhaps Fall. Does one have to pre-book any tour reservations? Any help would be appreciated as to where to start planning.

With 7-10 days, you can pretty much "see it all" in D.C. You could devote 1 day to seeing the memorials and either walk to them or take one of the hop on/hop off buses. (This would also be a good day to go to Arlington Cemetery. You can do this on your own or on one of the hop on/hop off buses.) Then you'll want to plan on a half day to a full day for each of the Smithsonian museums that interest you.
With this much time to spend in D.C., I'd plan on a trip to Mount Vernon (full day) and, if you have transporation, drive to Charlottesville for the day to visit Monticello.
Fall is a wonderful time here in D.C. The sky is blue, the weather is generally good, the summer crowds are gone and the crowds of students haven't started yet for the most part.
The only reservation which "must" be made in advance at that time of year is for a tour of the White House if you want to do that. But, you might want to consider arranging tours of the Capitol in advance through the office of your Representative. You can also get timed tickets in advance to go to the top of the Washington Monument and to tour Ford's Theatre which reopens in February. (See their respective websites for details.)

Fall is the best time to go. I think September is perfect. Or later in the fall, for the colors. 5-7 days is plenty. I suggest a side-trip to Williamsburg, Virginia.

With 7-10 days, and if you do a side trip to Williamsburg, I would also recommend visiting Jamestown and Yorktown.

I think a minimum half day at each museum, but preferably longer, if you want to do more than scratch the surface.

If you want to save more day time for museums, you can do a night tour of the memorials. We did "DC The Lights Tour" by OnBoard DC Tours. It went to more memorials than the others.

Mount Vernon was good. We took the Metro and bus out there and thought the surrounding areas were just lovely.

We pre-booked the National Archives to beat the line and my friend pre-booked the Spy Museum.

I have made many trips to DC and find late spring and early fall the best time to go. It is beautiful both times of the year and perfect walking weather.

When in DC, be ready to walk.

7-10 days is plenty of time. I agree that you could spend ages in DC and still not see it all. There is simply SO much to do there and a lot of it is truly a bargain or free.

Smithsonian Museums are great. I also recommend a visit to Arlington National Cemetery and the Iwo Jima Memorial. It is just a short metro ride.

As mentioned earlier, the only real "must" for a reservation is the White House.

Speaking of the metro, do not be shy about using it. It remains as one of the best rapid transit systems I have used.

A side trip to Williamsburg can be done, just make sure it is not too late in the fall. While they are "open" for a long season, much of the entertainment and action on the streets is centered around the summer tourist season. I go annualy and see a significant difference between the experience in June and the experience in October.

It is a great city. Enjoy!

You may also want to do a side-trip to Monticcelo. Absolutely beautiful.

Williamsburg, Monticello, and DC would be an interesting trio of destinations. The locations form a triangle, about 3 hours' travel time on each side.

It's very pretty at cherry blossom time. On the other hand, it can be very crowded with school groups and also can be very cold.

Thanks for the help - it's hard to know where to start sometimes! Since we're Nascar fans, we may include the Fall Richmond race in our plans. How long/congested a drive would it be to DC from Richmond?

The drive between DC and Richmond depends entirely on time of day and the day of the week. Generally, at any time, that stretch of I-95 is less than pleasant. Not that you shouldn't do it, though. Don't leave to head south during the week after about 3 pm. Don't head north during morning rush hour or on Sunday afternoons. If there are no problems or heavy traffic, it should take you between 2 and 2 1/2 hours.