  Topological superconductors are exotic gapped phases of matter hosting
Majorana mid-gap states on their boundary. In conventional topological
superconductors, Majorana in-gap states appear in the form of either localized
zero-dimensional modes or propagating spin-1/2 fermions with a
quasi-relativistic dispersion relation. Here we show that unconventional
propagating Majorana states can emerge on the surface of three-dimensional
topological superconductors protected by rotational symmetry. The
unconventional Majorana surface states fall into three different categories: a
spin-$S$ Majorana fermion with $(2S+1)$-fold degeneracy $(S\geq3/2)$, a
Majorana Fermi line carrying two distinct topological charges, and a quartet of
spin-1/2 Majorana fermions related by fourfold rotational symmetry. The
spectral properties of the first two kinds, which go beyond the conventional
spin-1/2 fermions, are unique to topological superconductors and have no
counterpart in topological insulators. We show that the unconventional Majorana
surface states can be obtained in the superconducting phase of doped $Z_2$
topological insulators or Dirac semimetals with rotational symmetry.
