We report the results of James Webb Space Telescope/NIRCam observations of 19 (sub)millimeter sources detected by the Atacama Large Millimeter Array (ALMA). The accurate ALMA positions allowed unambiguous identifications of their NIRCam counterparts. Taking gravitational lensing into account, these represent 16 distinct galaxies in three fields and constitute the largest sample of its kind to date. The counterparts' spectral energy distributions cover from rest-frame ultraviolet to near-IR and provide photometric redshifts (1 < z < 4.5) and stellar masses (M (*) > 10(10.5) M (circle dot)), which are similar to submillimeter galaxies (SMGs) studied previously. However, our sample is fainter in (sub)millimeter than the classic SMG samples are, and our sources exhibit a wider range of properties. They have dust-embedded star formation rates as low as 10 M (circle dot) yr(-1), and the sources populate both the star-forming main sequence and the quiescent categories. The deep NIRCam data allow us to study the rest-frame near-IR morphologies. Excluding two multiply imaged systems and one quasar, the majority of the remaining sources are disk-like and show either little or no disturbance. This suggests that secular growth is a potential route for the assembly of high-mass disk galaxies. While a few objects have large disks, the majority have small disks (median half-mass radius of 1.6 kpc). At this time, it is unclear whether this is due to the prevalence of small disks at these redshifts or some unknown selection effects of deep ALMA observations. A larger sample of ALMA sources with NIRCam observations will be able to address this question.