JPEG: Compressed quickly, results in a loss of detail and quality.
TIFF: Are bigger files, can be compressed.
RAW: Generally available on advanced compact cameras and DSLRs, compressed using a process that retains all the information originally captured.
DNG: You can store RAW files as DNG files by the Adobe DNG Convertor and you can keep them long-term
PNG: Retains all the digital detail, allows partial or total transparency.
GIF: Cannot contain more than 256 colors, good for animation and maintain only full transparency, not partial.
BMP: Invented by Microsoft and have larger file size because it saves color data in each individual pixel and is high quality, good for printing and not ideal for web usage.
PSD: Allows for manipulation on specific individual layers, you can do fine retouching using the layers which allows great flexibility when you can add, remove or edit any layers.