We report the analysis of HST WFPC2 F606W images of a sample of 35 spiral galaxies. We describe the optical morphological properties of the galaxies on scales of a few tens of parsecs, derive the surface brightness profiles for 18 of them, and present the results of analytical fits to these profiles. We find that: (I) Several galaxies, despite their classification as relatively early spirals, show little or no morphological evidence for a smooth, featureless (i.e., classical) bulge. Furthermore, even in the classical bulges, nuclear dust lanes are detected, similar to what is observed in early-type galaxies. (11) In several cases spiral structure reaches down to the innermost accessible scales. (III) A central, bright component is often identified. However, this does not resemble a classical bulge but has instead a highly irregular morphology. (IV) Bright knots, very likely star forming regions, are often present within the inner galactic regions in these irregular bulges. In several other cases, nuclear star formation is observed, but it is unclear whether this is associated with a small irregular bulge or with the inner disk. (V) Resolved, central compact sources are found in 18 of the 35 galaxies, including several early-type spirals. In two objects, NGC 1483 and NGC 3259, the central source is unresolved. Within the errors and the limited statistics, the central compact source luminosity seems independent of Rubble type, but correlates with the luminosity, of the disk galaxy. (VI) The central compact sources in star forming galaxies are typically brighter, for similar radii, than those in non star forming galaxies. (VII) The brightest compact sources have properties similar to those of young star clusters in the absolute magnitude (M_V) versus half-light radius (R_e) plane. The faintest compact sources are bracketed, in the M_V-R_e plane, between Kormendy's fit to elliptical galaxies and the correlation defined by classical R^1/4 bulges and Galactic globular clusters. The latter implies a roughly constant mean surface brightness within the effective radius. Therefore, the luminosity sequence of the compact sources might represent an age sequence of superluminous star clusters in the centers of disk galaxies. The widespread presence of star formation in the irregular bulges, the irregular bulges themselves, and the presence of superluminous star clusters in the nuclei of spirals, support scenarios in which a fraction of bulges forms relatively late, in dissipative accretion events driven by the disk.

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