We study droplet coalescence in a molecular system with a variable viscosity and a colloid-polymer mixture with an ultralow surface tension. When either the viscosity is large or the surface tension is small enough, we observe that the opening of the liquid bridge initially proceeds at a constant speed set by the capillary velocity. In the first system we show that inertial effects become dominant at a Reynolds number of about 1.5+/- 0.5 and the neck then grows as the square root of time. In the second system we show that decreasing the surface tension by a factor of 10(5) opens the way to a more complete understanding of the hydrodynamics involved.