The answer is not simple. It really depends on the circumstances and the file types in hand. For some categories the answer is simple in most cases. For example look at the multimedia category which includes audio and video files.
Most audio and video files are very big even relative to today storage devices and available bandwidth. Compression technology on the other and has advanced very much and very high compression ratios are available for audio and video files that hardly degrade the audio or video quality. So why not compress? It makes perfect sense to compress your multimedia files. In fact if you look for example at digital cameras and digital camcorders the default setting is for compression to be on. Image files coming out of digital cameras are by default compressed to a JPG format. Video files coming out of digital video camcorders are by default compressed to an MPG format.
In some rare cases compression of multimedia files in not wanted. This is especially true for professionals who process multimedia files by further processing audio images and videos. To ensure the best quality it is better to process raw multimedia files rather than compressed ones. But even professionals when done with the processing usually deliver the end result in a compressed format.
Some files types on the other hand are usually not worth compressing. Text files and word documents are rarely really too big and although compression can make them smaller it is not worth the time and effort. The same is true for executables and other binary files that do not tend to compress very well. If you can compress a file by half it is usually not worth the trouble.
Storage and bandwidth are available today for low price and great performances but even today storage is much more pervasive than bandwidth. Storing 1GB video files is not a big deal for most of us as default disk drives in home computers today are 100GB and more. But uploading or downloading a 1GB file is still a big deal that takes a long time to complete. If you need to move a 1GB file over the Internet for example compressing it is worth the effort and the processing time. Even reducing the file by 10 percent can significantly shorten the delivery time. The reason is simple the CPU time needed in order to compress a 1GB file is so much shorter than the time needed to transfer the saved 10 perfect or 100MB over any broadband home connection.
Compression utilities today are very simple to use. A few clicks and the file is compressed. Some big files like a 1GB data file can take minutes or more to compress but thanks to operating systems like Windows the compression task can run in the background at a lower priority letting you continue using the computer while the file is being compressed. Although compression software has many settings most of them balancing between speed and compression ratio usually it is best to keep the default as the extra compression of time saved by tweaking those utilities is usually insignificant for most cases.
Danette Mckay writes about this and many other subjects. Read more about 7z