PNG is a lossless compression format that is far more suitable as a GIF replacement than JPEG. It is ideal for non-photographic images with large sections of repetitive colours (e.g. screenshots, buttons). GIF is similar, but it only supports 256 colours. PNG is also required for any images with an alpha (opacity) mask, as neither JPEG nor GIF fully support this (neither did IE for years and years...before Firefox really caught on, Microsoft's browser team was asleep at the wheel and did nothing to fix any bugs).
However, for photographic (continuous-tone) images, PNG's compression is very weak, and much smaller files than are possible by judiciously throwing away some of the information that our eyes won't miss too much. This is the role that JPEG serves, and PNG does nothing to address that. I really don't think WebP will catch on, any more than the dud that is WebM, but as someone said earlier, it would be nice to have a format combining the size advantage of JPEG and the transparency features of PNG.
