BMP (Bitmap)
Arguably the most used, uncompressed format, it was originally used to handle the graphic files inside the Windows OS. This file format delivers large file sizes with lossless compression. Due to it being around for a while, BMP is widely recognized in Windows programs. Also because of it being introduced some time ago, BMP does not support transparencies.
GIF (Graphic Interchange Format)
A popular file format during the dark days of the internet (aka dial-up) for its very small file size, making it quick to load. GIF uses an 8bit colour
depth. Nowadays, because it supports animation, it is more widely
used to show animated clips, clips from movies (in a small image) and
other small animations, while keeping a small file size (and of course
very low image quality).
JPEG/JPG (Joint Photographic Experts Group)
JPEG is a lossy (an irreversible compression that approximates data in order to discard other bits of data, to reduce file size), it supports 8bit Grayscale and 24bit Colour images. While using JPEG you can choose whether to have a very small file size, but poor image quality, or a larger file size with better image quality. One shortcoming of JPEG is that the more you edit and save, the higher the generational degradation, which makes the quality look worse the more you edit it (even if you keep the same compression settings). Another shortcoming would be its inability to show transparency.
JPEG 2000
This format enables both lossy and lossless compression. Even though the names might be similar, JPEG/JPG and JPEG 2000 use very different compression methods. JPEG 2000 has better quality and compression rations, but uses significantly more computational power.
TIFF (Tagged Image File Format)
TIFF is more flexible than most formats and supports 24bit or 48bit colour images. TIFF can be lossy or lossless and has good compression algorithms. Unfortunately TIFF is not widely supported by Web Browsers. Due to it's tagged structure, TIFF is preferred in Photography and Printing, as it can retain a lot more information. Of course this also makes TIFF one of the larger file sizes.
PNG (Portable Network Graphics)
This file format is the most popular file format, on the internet, now a days. It has, for the most part, replaced GIF when it comes to displaying images online, or images with transparency in them, PNG also supports 24bit and 48bit truecolor, and alpha channels. PNG can also support animation, under the form of MNG and APNG file formats.
