From what point could you view the most US states?

Rock City, Lookout Mountain, GA. There were signs all over the Midwest (and probably South, and East, etc) for decades that claimed you could see seven states from Lookout Mountain, GA.

I honestly doubt this was ever the case, but the jury may still be out.

The four corners area would be one spot where you would be guaranteed to see four states (New Mexico, Arizona, Utah, Colorado). It already is a tourist attraction.

Perhaps there may be a spot in the Appalachian Mountains in southern part of New Hampshire or Vermont, where on a really clear day you might be able to see five states. But this is just a guess based on topography.

While Four Corners would be the only one where 4 states visibility is guaranteed, on a clear day you can see 4 states from the Skydeck of Willis (Sears) Tower in Chicago:

On a clear day, you can see four states – Illinois, Indiana, Wisconsin and Michigan. Visibility from the Skydeck is approximately 40-50 miles (65 – 80 kilometers).

The Four Corners Monument...

The Navajo Nation cordially welcomes you to one of our most unique landmarks - The Four Corners. This is the only place in the United States where four states intersect at one point: Arizona, New Mexico, Utah and Colorado. This location is very remote as you will experience when visiting.

The original marker erected in 1912 was a simple cement pad, but has since been redone in granite and brass. The Visitor Center is open year round, and features a Demonstration Center with Navajo artisans. Navajo vendors sell handmade jewelry, crafts and traditional Navajo foods nearby.

Source: http://www.navajonationparks.org/htm/fourcorners.htm

Also see the Wiki article: http://en.wikipedia.org/wiki/Four_Corners_Monument

If you consider a man-made tower there was Wonder Tower in Genoa, Colorado (now closed) in Eastern Colorado that you could see 6 States - Colorado, Kansas, Nebraska, Wyoming, New Mexico and South Dakota:

http://ourjourney.info/MyJourneyDestinations/WonderTower.asp

http://www.roadsideamerica.com/story/2050

From the top of Mt Rogers (highest point VA) in ideal viewing conditions, one can see 5 states; VA, WV, KY, TN & NC

The furthest is KY about 70 miles away.

Mt rogers is a very popular spot for hikers (on the Appalachian trail) and horse riders, but no road access.

From the International Space Station you can see all 50 states at once. It is a tourist destination but ticket prices are... astronomical.

Related question on Space.SE:
How could I travel to space as an ordinary citizen?

There is a point in Western Oklahoma, near Boise City that is within 30 miles of five different states. If you were about 500 feet above the ground there, you'd be able to see Kansas, New Mexico, Oklahoma, Texas, and Colorado.

A quick glance at Google Street View shows no skyscrapers, but small hills, probably less than 500 feet tall.