Unlike vector data exchange formats, we have a general, all-purpose, widely supported raster format--GeoTIFF. Due to the existence and popularity of the highly capable TIFF specification for storing lossless image data, it was extended to store spatial data along their metadata (for example, projection and georeferencing). There are only two drawbacks of this format--its size and the web. As it only supports a few compressing methods, its lossy JPEG compression cannot race, for example, with the JPEG2000 standard if data loss is acceptable. Furthermore, web browsers cannot handle TIFF files; therefore, rasters have to be converted to regular images before using them in a web client application.
GeoTIFF offers a lot of options to work with. It can create internal pyramids for various resolutions for faster visualization. It can also utilize internal tiling to speed up processing when the raster is very large. It can even compress data with various algorithms. There are some lossless options like LZW or deflate (ZIP), and there is the lossy JPEG compression for a significantly smaller file size.