No, you should not compress your hard drive.
Compressing your hard drive may save you some space. However, compression is a two-part process: compression and decompression. Although decompression isnt as taxing on the computer as compression, it still requires CPU, RAM, and disk cycles. This can cause video and audio playback to become stuttered. Disk compression is best used on files that you are not likely to frequently access.
What you should look at are video codecs and audio codecs. A codec is software that enables compression or decompression of digital media. Codecs are a can be both lossy and non-lossy compression formats, but that doesnt necessarily mean the video/audio will be noticeably degraded. Video and audio codecs can strip out data that the humans cant see or hear. The most common example are MP4 videos and MP3 audio. DVD and BluRay videos are compressed with codecs as is the music you buy from online stores.
Im not saying disk compression isnt a solution, its just not the right tool for the job. You dont use a steam roller to hammer a nail.