Laboratory searches for the detection of gravitational waves have focu
sed on the detection of burst signals emitted during a supernova explo
sion but have not resulted in any confirmed detections. An alternative
approach has been to search for continuous wave (CW) gravitational ra
diation from the Crab pulsar. In this paper, we examine the possibilit
y of detecting CW gravitational radiation from pulsars and show that n
earby millisecond pulsars are generally much better candidates. We sho
w that the minimum strain h(c) similar to 10(-26) that can be detected
by tuning an antenna to the frequency of the millisecond pulsar PSR 1
957+20, with the detector technology available at present, is orders o
f magnitude better than what has been accomplished so far by observing
the Crab pulsar, and is within an order of magnitude of the maximum s
train that may be produced by it. In addition, we point out that there
is likely to be a population of rapidly rotating neutron stars (not n
ecessarily radio pulsars) in the solar neighborhood whose spin-down ev
olution is driven by gravitational radiation. We argue that the projec
ted sensitivity of modern resonant detectors is sufficient to detect t
he subset of this population that lies within 0.1 kpc of the Sun.