We present ground-based B- and R-band color-magnitude diagrams (CMDs) reaching the oldest main-sequence (MS) turnoffs with good photometric accuracy for 12 fields in the Small Magellanic Cloud (SMC). Our fields, located between ~1° and ~4° from the center of the galaxy, are situated in different parts of the SMC such as the ``Wing'' area and toward the west and south. In this paper we perform a first analysis of the stellar content in our SMC fields through comparison with theoretical isochrones and color functions (CFs). We find that the underlying spheroidally distributed population is composed of both intermediate-age and old stars and that its age composition does not show strong galactocentric gradients. The three fields situated toward the east, in the Wing region, show very active current star formation. However, only in the eastern field closest to the center do we find an enhancement of recent star formation with respect to a constant SFR(t). The fields corresponding to the western side of the SMC present a much less populated young MS, and the CF analysis indicates that the SFR(t) greatly diminished around 2 Gyr ago in these parts. Field smc0057, the closest to the center of the galaxy and located in the southern part, shows recent star formation, while the rest of the southern fields present few bright MS stars. The structure of the red clump in all the CMDs is consistent with the large amount of intermediate-age stars inferred from the CMDs and color functions. None of the SMC fields presented here are dominated by old stellar populations, a fact that is in agreement with the lack of a conspicuous horizontal branch in all these SMC CMDs. This could indicate that a disk population is ruling over a possible old halo in all the observed fields.