  We report the results of a spectroscopic search for debris disks surrounding
41 nearby solar type stars, including 8 planet-bearing stars, using the {\it
Spitzer Space Telescope}. With accurate relative photometry using the Infrared
Spectrometer (IRS) between 7-34 $\micron$ we are able to look for excesses as
small as $\sim$2% of photospheric levels with particular sensitivity to weak
spectral features. For stars with no excess, the $3\sigma$ upper limit in a
band at 30-34 $\mu$m corresponds to $\sim$ 75 times the brightness of our
zodiacal dust cloud. Comparable limits at 8.5-13 $\mu$m correspond to $\sim$
1,400 times the brightness of our zodiacal dust cloud. These limits correspond
to material located within the $<$1 to $\sim$5 AU region that, in our solar
system, originates from debris associated with the asteroid belt. We find
excess emission longward of $\sim$25 $\mu$m from five stars of which four also
show excess emission at 70 $\mu$m. This emitting dust must be located around
5-10 AU. One star has 70 micron emission but no IRS excess. In this case, the
emitting region must begin outside 10 AU; this star has a known radial velocity
planet. Only two stars of the five show emission shortward of 25 $\micron$
where spectral features reveal the presence of a population of small, hot dust
grains emitting in the 7-20 $\mu$m band. The data presented here strengthen the
results of previous studies to show that excesses at 25 $\micron$ and shorter
are rare: only 1 star out of 40 stars older than 1 Gyr or $\sim 2.5$% shows an
excess. Asteroid belts 10-30 times more massive than our own appear are rare
among mature, solar-type stars.
