The changing view of planets orbiting low mass stars, M stars, as potentially hospitable worlds for life and its remote detection was motivated by several factors, including the demonstration of viable atmospheres and oceans on tidally locked planets, normal incidence of dust disks, including debris disks, detection of planets with masses in the 5-20 M() range, and predictions of unusually strong spectral biosignatures. We present a critical discussion of M star properties that are relevant for the long- and short-term thermal, dynamical, geological, and environmental stability of conventional liquid water habitable zone (HZ) M star planets, and the advantages and disadvantages of M stars as targets in searches for terrestrial HZ planets using various detection techniques. Biological viability seems supported by unmatched very long-term stability conferred by tidal locking, small HZ size, an apparent short-fall of gas giant planet perturbers, immunity to large astrosphere compressions, and several other factors, assuming incidence and evolutionary rate of life benefit from lack of variability. Tectonic regulation of climate and dynamo generation of a protective magnetic field, especially for a planet in synchronous rotation, are important unresolved questions that must await improved geodynamic models, though they both probably impose constraints on the planet mass. M star HZ terrestrial planets must survive a number of early trials in order to enjoy their many Gyr of stability. Their formation may be jeopardized by an insufficient initial disk supply of solids, resulting in the formation of objects too small and/or dry for habitability. The small empirical gas giant fraction for M stars reduces the risk of formation suppression or orbit disruption from either migrating or nonmigrating giant planets, but effects of perturbations from lower mass planets in these systems are uncertain. During the first approximately 1 Gyr, atmospheric retention is at peril because of intense and frequent stellar flares and sporadic energetic particle events, and impact erosion, both enhanced, the former dramatically, for M star HZ semimajor axes. Loss of atmosphere by interactions with energetic particles is likely unless the planetary magnetic moment is sufficiently large. For the smallest stellar masses a period of high planetary surface temperature, while the parent star approaches the main sequence, must be endured. The formation and retention of a thick atmosphere and a strong magnetic field as buffers for a sufficiently massive planet emerge as prerequisites for an M star planet to enter a long period of stability with its habitability intact. However, the star will then be subjected to short-term fluctuations with consequences including frequent unpredictable variation in atmospheric chemistry and surficial radiation field. After a review of evidence concerning disks and planets associated with M stars, we evaluate M stars as targets for future HZ planet search programs. Strong advantages of M stars for most approaches to HZ...