For hexadecane oil droplets at an aqueous-air surface, the surface film in coexistence with the droplets exhibits two-dimensional gaseous (G), liquid (L), or solid (S) behavior depending upon the temperature and concentration of the cationic surfactant dodecyltrimethylammonium bromide. In the G (L) phase, oil droplets are observed to coalesce (fragment) as a function of time. In the coalescence region, droplets coalesce on all length scales, and the final state is a single oil droplet at the aqueous-air surface. The fragmentation regime is complex. Large oil droplets spread as oil films; hole nucleation breaks up this film into much smaller fluctuating and fragmenting or metastable droplets. Metastable droplets are small contact angle spherical caps and do not fluctuate in time; however, they are unstable over long time periods and eventually sink into the bulk water phase. Buoyancy forces provide a counterbalancing force where the net result is that small oil droplets (radius r < 80 mu m) are mostly submerged in the bulk aqueous medium with only a small fraction protruding above the liquid surface. In the G phase, a mechanical stability theory for droplets at liquid surfaces indicates that droplet coalesce is primarily driven by surface tension effects. This theory, which only considers spherical cap shaped surface droplets, qualitatively suggests that in the L phase the sinking of metastable surface droplets into the bulk aqueous medium is driven by a negative line tension and a very small spreading coefficient.