The Gelfand-Kirillov dimension of an algebra is either zero, one, or at least $2$.

This sounds silly, but one has to remember that the GKdim is a real number (or $\infty$) and that there are algebras with GKdim equal to $r$ for all real $r\geq2$.

This is a combination of results of several people. See the books by McConnell and Robson, or by Krause and Lenagan.