The two most common formats on the web are JPG and PNG. In general, PNG is a higher-quality compression format. JPG images are generally of lower quality, but are faster to load. These factors affect whether you decide to use PNG or JPG, as does what the image contains and how it will be used.
If you are submitting a design to use to use for printing we suggest any of these file types: .png, .jpeg, .ai, .psd, and .pdf, as high resolution as possible.