What Palin really said:

“They’re our next door neighbors. And you can actually see Russia from land here in Alaska.”

As to the question of whether one can actually see Russia from Alaska, Governor Palin was correct: such a view is possible from more than one place in Alaska. A Slate article on the topic noted that:

In the middle of the Bering Strait are two small, sparsely populated islands: Big Diomede, which sits in Russian territory, and Little Diomede, which is part of the United States. At their closest, these two islands are a little less than two and a half miles apart, which means that, on a clear day, you can definitely see one from the other.

http://www.snopes.com/politics/palin/seealaska.asp