I am specifically interested in software that can be used to combine existing sets of images (frames in the animation) into an animation. Having the ability to add transitions/effects between the frames would be a plus. The output format should be something suitable for the web, e.g. GIF, Flash.
Please comment on ease-of-use, number of features, personal user experience, cost of software (free/paid) and which OS it runs on when you mention the programs.