Looking forward to " see" or "seeing"?

Which of the 2 sentences is correct?

Sam is looking forward to see the Rocky mountains.

Sam is looking forward to seeing the Rocky mountains.

In the example you gave, "to seeing" is correct. To understand why, let's think about different meanings of the word to.

• To can be part of a verb in the infinitive: "To be or not to be,..." or "I can't wait to see the Rocky Mountains." The to is part of the action.
• To can also be a preposition, a word that demonstrates a relationship with something. Here that something is "seeing the Rocky Mountains", it's what Sam is looking forward to — seeing is a thing, it is a noun.

By the way, the M in "Rocky Mountains" should be capitalized, it's part of the place name.