  We present the timing and spectral analyses of theXMM-newton data on the
17-Myr-old, nearby radio pulsar B0950+08. This observation revealed pulsations
of the X-ray flux of the pulsar at its radio period. The pulse shape and pulsed
fraction are apparently different at lower and higher energies of the observed
0.2-10 keV energy range, which suggests that the radiation cannot be explained
by a single emission mechanism. The X-ray spectrum of the pulsar can be fitted
with a power-law model with a photon index about 1.75 and an (isotropic)
luminosity about 9.8e29 erg/s in the 0.2-10 keV. Better fits are obtained with
two-component, power-law plus thermal, models with index of 1.30 and 9.7e29
erg/s for the power-law component that presumably originates from the pulsar's
magnetosphere. The thermal component, dominating at E>0.7 keV, can be
interpreted as radiation from heated polar caps on the neutron star surface
covered with a hydrogen atmosphere. The inferred effective temperature, radius,
and bolometric luminosity of the polar caps are about 1 MK, 250 m, and 3e29
erg/s. Optical through X-ray nonthermal spectrum of the pulsar can be described
as a single power-law with index 1.3-1.4 for the two-component X-ray fit. The
ratio of the nonthermal X-ray (1-10 keV) luminosity to the nonthermal optical
(4000-9000 \AA) luminosity is within the range of 1e2-1e3 observed for younger
pulsars, which suggests that the magnetospheric X-ray and optical emissions are
powered by the same mechanism in all pulsars. An upper limit on the temperature
of the bulk of the neutron star surface, inferred from the optical and X-ray
data, is about 0.15 MK. We also analyze X-ray observations of several other old
pulsars, B2224+65, J2043+2740, B0628-28, B1813-36, B1929+10, and B0823+26.
