Using stimulus-sensitive microgel particles as an emulsifier, we have prepared a new type of emulsion responsive to pH, ionic strength, and temperature changes. Each of these environmental changes can trigger a volume phase transition in poly(N-isopropylacrylamide) (PNIPAM) microgel particles containing some carboxylic groups. Depending on their hydrophobicity and charging state, such PNIPAM microgel particles can adsorb to the droplets of an octanol-in-water emulsion and provide excellent stability against coalescence and ripening. We have studied in detail the correlation between the particles' response to changes in the solution conditions and the corresponding response of particle-decorated emulsion droplets. In their swollen, hydrophilic state, the microgel particles consistently stabilize the octanol droplets, but inducing a microgel collapse usually results in a destabilization of the emulsion and eventually in phase separation. A notable exception was found at high pH where particles are highly charged: in this regime emulsions remain stable even upon a temperature-induced collapse of the microgel particles and prove sensitive only to high levels of screening ions. Microscopy studies of toluene-in-water emulsions stabilized by compact polystyrene particles of variable surface charge further suggest an intimate connection between the charge and packing density of interfacial particles and hint at a charge-induced interparticle attraction.