Some basic background information on compression:
Truly random data is not losslessly compressible at all. This is something of a basic tenet of a field of study known as Information Theory (closely related to Computer Science). For a file to be losslessly compressible, its data must be repetitive or predictable.
One rule of thumb is that arbitrary computer files are typically around 50% compressible using a decent lossless algorithm. Text files are often dramatically compressible.
If you have pictures, audio, or video files, they may be able to be dramatically compressed while still remaining reasonable fidelity to the original if you can accept lossy compression. The lossy compression algorithms vary based on the medium (still photos, audio, video, etc.), and even by the sub-category; a photo from a camera might be best compressed with JPEG, whereas a computer graphic might be best compressed with a different codec. Music does best with codecs like MP3 or AAC at bitrates of 256kbps or higher, but voice recordings can be compressed to just 9.6kbps and still be perfectly intelligible.
The H.264 AVC codec can compress HD video by two or almost three orders of magnitude (that is, to less than 1% of its original size) while still retaining reasonable quality. Uncompressed full HD is 1920 pixels wide * 1080 pixels high * 24 bits/pixel * 30 frames per second = about 1.5 gigabits per second, but it's not uncommon to see H.264 AVC compressed HD at 15 megabits per second or less with reasonable image quality.
If you compress a file once (lossy or lossless), and then try to do a lossless compression of that, it tends to not be capable of much further compression. That's because any good compression algorithm should have gotten rid of all the wasted space (repetitive or unnecessary data), so there shouldn't be anything left to compress.