Can tourists visit the White House or the US Capitol Building?

For the White House, according to Wikitravel:

President Jefferson opened the White House to the public, and it has remained so during peacetime (with varying restrictions) ever since. Following the attacks of September 11th, tours have been available only for groups of ten or more, and these must be requested up to six months in advance through your congressman if you're a US citizen, or through your country's embassy in Washington D.C. if you're a foreigner.

From the White House website:

Public tours of the White House are available. Requests must be submitted through one's Member of Congress. These self-guided tours are available from 7:30 a.m. to 11:00 a.m. Tuesday through Thursday, 7:30 a.m. to 12:00 p.m. Fridays, and 7:30 a.m. to 1:00 p.m. Saturdays (excluding federal holidays or unless otherwise noted). Tour hours will be extended when possible based on the official White House schedule. Tours are scheduled on a first come, first served basis. Requests can be submitted up to six months in advance and no less than 21 days in advance. You are encouraged to submit your request as early as possible as a limited number of spaces are available. All White House tours are free of charge. (Please note that White House tours may be subject to last minute cancellation.)

If you wish to visit the White House and are a citizen of a foreign country, please contact your embassy in Washington, DC for assistance in submitting a tour request.

The US Capitol building depends on whether you want a self-guided tour, organised, and what you want to see. For information on tours available, and the online booking system, there's a handy website. Tours are free, but need to be booked in advance (usually) as they can fill up fast, depending on the time of year and occasion.

So it's been a while sense this was last answered and some things have changed...

White House: Sorry, no more tours! You can thank the sequester for that. You can, however, get in if the President invites you, or you are doing official business. I live 30min away from DC and I have a friend who gets to go to the White House Christmas Dinner every year so it is possible to get in. You can also go when they have events, like Easter Monday on the White house Lawn.

Capitol Building: This one is easy to get in to see. Just go to the East side of the building to the visitors entrance, get in line, and buy a ticket! You'll get a time to report back for the tour, so I would buy them online so you can pick a good time for yourself. However, a better option is to go see your senator/representative in one of the office buildings next to the capitol. There you can actually meet someone important and you get a private tour of the capitol building by their intern (My high school has a class where you actually get an internship on the hill). You also get tickets to see the senate and the house, which you can only get via talking to your senator/representative. You get to ride the secret subway that takes people back and forth from the offices to the Capitol Building.

Also, while you are in the area, I'd recommend checking out the Library of Congress which is right across the street. You can get to it from the Capital Building via underground tunnel which is really cool (literally).

Also, if you have time, most senate hearings and almost all Supreme Court hearings are open to the public. Take a look on their respective websites to see what they are discussing that day. They can be really fun and who knows, you might even get into one of the medias pictures, securing your spot in history.