We present upper limits on the local ionizing background based on a search for extended H alpha emission from three nearby intergalactic H I clouds: the Leo Ring (M96 group), both the NE and SW lobes of the Haynes-Giovanelli Virgo Cloud (H I 1225 + 01), and the H I tidal tails associated with the NGC 4631/4656 group. These clouds were chosen to have 21 cm emission that is extended (10-100 kpc) and distant from any associated galaxy. Deep, wide-field CCD images were acquired through narrow- ( similar to 31 Angstrom) and broadband R filters with the Burrell Schmidt telescope on Kitt Peak. We set a 95% confidence upper limit on the H alpha surface brightness for the areas of the clouds detected in H I of 1.6 x 10(-19) ergs s(-1) cm(-2) arcsec(-2) in Leo and of 3.7 x 10(-19) ergs s(-1) cm(-2) arcsec(-2) in Virgo. We limit the local ionizing background to Phi(0) < 5.0 x 10(3) photons s(-1) cm(-2) sr(-1) (95%) at the location of the Leo Ring cloud and Phi(0) < 1.1 X 10(4) photons s(-1) cm(-2) sr(-1) at the Virgo cloud, assuming spherical clouds. (Limits are a factor of 2 higher for a thin face-on slab.) The limits correspond to J(0) < 3.3 X 10(-23) and 7.6 x 10(-23) ergs s(-1) cm(-2) sr(-1) Hz(-1) for a nu(-1/2) spectrum (1.6 times higher for a v(-1.4) spectrum) between 1 and 4 ryd. Such low limits suggest that quasar light, and not galactic light, dominates the ionizing background at low redshift. The H alpha limit on the Leo cloud is significantly below a previously reported detection. In the field of the edge-on galaxies NGC 4631 and NGC 4656, we detect H alpha from ionized gas extending nearly 16 kpc above N4631, which could have been blown out by starburst activity in the plane, and a low surface brightness companion or stellar tidal tail. This companion lies between N4631's H I tidal tails and may have played a role in creating the H I tidal tails, or it may represent star formation within the tidal tails. We also report the tentative detection of an ultrafaint ''sheet'' of H alpha emission extending from NGC 4631 to NGC 4656.