Synfig Studio is a powerful open source application for creating high quality 2D animations with bitmap and vector graphics.
The program speeds up the animation process by removing the need to create each frame individually. Instead you can have Synfig Studio generate your frames itself by morphing from one image to another, or applying one or more transformations to individual shapes (rotation, scale etc).
Alternatively, if you'd like to use a frame-by-frame source, the program's tracing tools will help you convert it into vector shapes which you can then manipulate with its other tools.
Features include a comprehensive bone system, bitmap painting engine, path-based gradients, a wide range of layers ("geometric, gradients, filters, distortions, transformations, fractal and a few others"), while High Dynamic-Range Imaging reportedly delivers "better lighting effects, and improved color composition".
Version 1.3.2 changes include:
Synfig Studio is a versatile application which can help you produce anything from a simple web animation (move this object from here to there) to a professional film-quality animated movie. It's also vast and takes time and effort to learn, but if you have the motivation then there's plenty of high quality documentation to explore.