  We analyze pairing of fermions in two dimensions for fully-gapped cases with
broken parity (P) and time-reversal (T), especially cases in which the gap
function is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$
(p-wave, spinless or spin-triplet) and $l=-2$ (d-wave, spin-singlet). For
$l\neq0$, these fall into two phases, weak and strong pairing, which may be
distinguished topologically. In the cases with conserved spin, we derive
explicitly the Hall conductivity for spin as the corresponding topological
invariant. For the spinless p-wave case, the weak-pairing phase has a pair
wavefunction that is asympototically the same as that in the Moore-Read
(Pfaffian) quantum Hall state, and we argue that its other properties (edge
states, quasihole and toroidal ground states) are also the same, indicating
that nonabelian statistics is a {\em generic} property of such a paired phase.
The strong-pairing phase is an abelian state, and the transition between the
two phases involves a bulk Majorana fermion, the mass of which changes sign at
the transition. For the d-wave case, we argue that the Haldane-Rezayi state is
not the generic behavior of a phase but describes the asymptotics at the
critical point between weak and strong pairing, and has gapless fermion
excitations in the bulk. In this case the weak-pairing phase is an abelian
phase which has been considered previously. In the p-wave case with an unbroken
U(1) symmetry, which can be applied to the double layer quantum Hall problem,
the weak-pairing phase has the properties of the 331 state, and with nonzero
tunneling there is a transition to the Moore-Read phase. The effects of
disorder on noninteracting quasiparticles are considered.
