We wondered the same thing when my son turned one. He wasn't going to know that it was his party and our friends and family had been overly generous at THREE showers, when he was born and at his baptism.
So... after talking with both of our mothers, we asked them to spread the word to those who they were in contact with that we wanted to keep the gifts from becoming overwhelming. As the "grandmas" they sent a note to the families inviting people to contribute to a large gift (swing set and sand box). It worked better than we thought!
Instead of a pile of gifts from tons of relatives, JD got a swing set and some other outdoor toys that he loves. He had gifts to open b/c the letter only went to family, so he had the best of both worlds.
Our moms are doing the same for Christmas- this time for a train set. You'd be surprised by how many people are responsive to this idea.