We used a three-dimensional smooth-particle hydrodynamics (SPH) code with 7000 particles to simulate 30 collisions between lower main-sequence (MS) stars whose masses differ by a factor of 5. We also simulated encounters with point-mass intruders to understand better how the finite radius of the intruder affects the dynamics. The two MS stars become gravitationally bound in a physical collision if their relative velocity, V, at infinity is less than a critical (dissipation) velocity, V(d). We find that V(d) decreases from 1000 km s-1 in a head-on collision to 150 km s-1 in a grazing one. If the less massive star is replaced by a point mass (e.g., a white dwarf), V(d) remains the same for grazing collisions and tidal encounters, but it drops to approximately 600 km s-1 in head-on collisions. If V > V(d), the lower mass ms star, which is the denser of the two, passes through the more massive MS star and escapes without becoming gravitationally bound to it. In collisions between two main-sequence stars, V(d) increases with V due to increased shock dissipation. In collisions between a point mass and a main-sequence star, V(d) decreases as V increases. The only dissipation in these cases is by gravitationally induced oscillations that decrease in importance as V increases. If the two MS stars coalesce in a physical collision, the denser (lower mass) MS star settles to the center of the other one. The violent mixing of the more massive star during the encounter and the settling of the low-mass star to its center should reset the nuclear clock of the coalesced star, so it contracts to the (helium-rich) MS. The fraction of the stellar mass lost in these collisions is much less than that lost in collisions between stars of equal mass and density. In particular, grazing collisions do not produce the large mass loss and accretion disks that characterize collisions between equal-mass stars. We find that tidal captures of binary stars in globular clusters can only occur in encounters in which the closest approach of the two stars to their center of mass is less than 2.0 times the sum of their radii. Coalescence of two MS stars in a globular cluster is more probable than their forming a binary by tidal capture. Tidal capture is not possible if the impact velocity at infinity exceeds 150 km s-1. Even at zero impact velocity, the coalesced star acquires a kick velocity of up to 4.5 km s-1 by asymmetric jetting during the collision. This velocity is not enough to eject the coalesced star from a globular cluster, but it largely compensates for the dynamical cooling resulting from the coalescence of the two stars. The coalescence of stars in globular clusters does not speed up the dynamical collapse of the core of the cluster.
