Traditional file formats are GIF and JPEG.
GIF files are limited to a 256 colour indexed pallet. One colour may be set as a transparency. The compression method for these files is non-lossy and best suited to images to areas of the same colour (eg. clipart, logos, icons). Transparent GIFs will only work against solid backgrounds of a pre-determined colour. For example, a GIF set to be transparent over white will have a halo effect of dithered pixels when placed over black.
JPEG files may have millions of colours is a 24-bit format. If you reduce the bit depth, smaller sized files are available at the expense of the number of colours. JPEG files do not support transparencies. JPEG files have an excellent compression algorithm. Although somewhat lossy, 10:1 compression savings are common (compared to raw or non-compressed TIFF images).
Both GIF and JPEG support progressive downloads, but the JPEG format is not well supported.
I don't think GIF or JPEG files can store a colour profile (used for consistent colours on different computers, monitors and operating systems).
PNG is a 24-bit (millions of colours) replacement for GIF. Since it is not patented, most open-source programs favour this format. It supports an alpha layer transparency which allows for perfect transparencies on any background.
I don't think it supports progressive downloads. File sizes tend to be twice as large as GIF images and ten or fifteen percent larger than JPEGs (guessing). <== Would someone on this forum like to test those assumptions.
It is well supported by IE5+ and NS7+.
This file format is suitable as a replacement for GIF and JPEG.
SVG is a format for vector art. If preserving your vector artwork, or generative large dimension images in a small size, is important. This format is for you. I think a plug-in is required...
Does this help?