We present the initial results of a program to obtain high resolution images of Seyfert galaxies with the Planetary Camera aboard the Hubble Space Telescope (HST). In this paper we discuss the images of the type 2 Seyfert NGC 5929 and the type 1.5 Seyfert MCG 8-11-11 (= UGC 3374). The images were obtained in the emission lines of (O III) lambda lambda 4959 and 5007 A and H alpha + (N II) lambda lambda 6548 and 6583 A and their adjacent continua. The high-excitation gas in the narrow line region (NLR) of NGC 5929 is resolved into individual clouds in the central 1 sec .5. Although the (O III) emission is clearly not spherically symmetric with respect to the nucleus, it does not define a distinct 'bicone' morphology, as observed by the HST in a few other Seyfert galaxies. We find no direct evidence for the reddening and/or obscuration effects characteristic of a dusty torus, which, in the context of 'unified models', is expected to obscure the active galactic nucleus (AGN) in type 2 Seyfert galaxies. The correspondence between the emission line gas and the radio morphology suggests that the structure of the NLR in NGC 5929 is governed by matter ejected from the AGN. A comparison of the recombination rate of hydrogen in the brightest emission line cloud with an upper limit on the ionizing luminosity emitted toward Earth provides no evidence that the central ionizing source radiates anisotropically. The images of MCG 8-11-11 show only an unresolved nuclear source. No emission line gas associated with the extended radio source is detected. We estimate upper limits on the intensity of extended line emission in this galaxy and examine their significance.