I've often used Inquisit to run psychological experiments online. The software enables delivery of stimuli (e.g., text, images, etc.) and collection of reaction times.
Obviously general purpose programming languages provide one avenue for delivery of online experiments. There's also a good listing of software for psychological experiments here. I've also seen PsyToolkit which is GNU licensed software for programming psychological experiments, but I'm not aware of any online option.
Are there any open source options for online delivery of psychological experiments, particularly ones that enable reaction time measurement?