We present a general class of self-similar solutions of the full set o
f MHD equations that include matter flow, electromagnetic fields, pres
sure, and gravity. The solutions represent axisymmetric, time-independ
ent, nonrelativistic, ideal, magnetohydrodynamic, collimated outflows
(jets and winds) from magnetized accretion disks around compact object
s. The magnetic field extracts angular momentum from the disk, acceler
ates the outflows perpendicular to the disk, and provides collimation
at large distances. The terminal outflow velocities are of the order o
f or greater than the rotational velocity of the disk at the base of t
he flow. When a nonzero electric current flows along the jet, the outf
low radius oscillates with axial distance, whereas when the total elec
tric current is zero (with the return current flowing across the jet's
cross section), the outflow radius increases to a maximum and then de
creases. The method can also be applied to relativistic outflows.