Subarcsecond observations using the Very Large Array (VLA) are presented for low-luminosity H₂O maser emission in M82, M51, and NGC 4051. New maser features have been detected within the M82 starburst complex. They are largely associated with star-forming activity such as optically identified starburst-driven winds, H II regions, or the early phase of star formation in the galaxy. The H₂O maser in M51 consists of blueshifted and redshifted features relative to the systemic velocity of the galaxy. The redshifted features are measured to the northwest of the nuclear radio source, while the location of the blueshifted counterpart is displaced by ~2'' from the radio source. A small velocity gradient closely aligned with the radio jet is detected from the redshifted features. The redshifted maser most likely amplifies the background radio continuum jet, while the blueshifted counterpart marks off-nuclear star formation in the galaxy. All of the detected maser features in the narrow-line Seyfert 1 galaxy NGC 4051 remain unresolved by new VLA observations. Due to the low luminosity of the maser, the maser excitation is not directly related to the active galactic nucleus.