The ability to merge two droplets is an important component of droplet-based lab-on-a-chip devices, yet flow-induced coalescence is difficult to achieve due to long film drainage times compared with relatively short residence times. We examine droplet collisions at a simple microfluidic T-junction and characterize the response for a wide range of droplet sizes and speeds. We find that three primary responses occur, where coalescence occurs easily at low collision speeds, smaller droplets traveling faster slip past one another without coalescing, and larger and faster droplets can break one another into multiple segments. The critical capillary number for coalescence agrees well with previously reported scaling for isolated droplet pairs when local curvature and speed are taken into account. The critical capillary number for splitting of droplets agrees well with a previously reported stability condition for individual droplets stretching in an extensional flow. Quantifying the necessary conditions for coalescence and non-coalescence behavior should enable the informed design of lab on chip devices based on discrete liquid segments.