Most image files (such as JPEG, GIF, and PNG) are already as compressed as they can be. You can use a compression program like Winzip, Winrar, or 7z, but it will have little or no effect.
JPEG provides the most compression, since you can set the quality lower, which loses detail.
If you are trying to email photos taken with a digital camera, you may want to save a lower-resolution copy, e.g. reduce the resolution from 3000x2000 to 1000x800. That will reduce the size tremendously. Of course the recipient isn't getting all the detail in the original file.