Choosing the Right Tools
There are several things that you need to consider when looking for a tool to compress files:
Compression ratio. Some file archivers will produce smaller files. Many archiving tools will let you choose the level of compression and/or the format of the compressed file. Better compression often comes at the cost of decreased speed. Note that some types of files - e.g. music in the mp3 format and video files - can't be compressed effectively with general purpose archivers. A good file archiver should offer high compression ratio and the ability to set it manually, so as to give you some control over how long the archiving will take.
Supported formats. Most people skip over this crucial point when choosing an archiver. While the most popular format is ZIP, you're likely to encounter many different (and sometimes better) file formats if you ever download files from the Internet. For example, the RAR format, which offers good compression, is relatively common on the web and in BitTorrent downloads. BZ2, TAR and GZ are popular among the users of Unix-based systems. And that's just from the top of my head - there are actually dozens more. A good archiving tool should know how to compress files using some popular formats (like ZIP) and should be able to open all popular file formats.
Cost. Last, but not the least, there's the matter of price. This is something you'll need to decide yourself. File archivers aren't the most expensive kind of software, so you can probably find a good shareware archiver in the $20-$50 range. Alternatively, if all you need is a simple tool that knows how to compress files (and decompress them later, too), you can opt for one of the freeware archivers. Though they may lack the shiny user interface and "extra" functions (which mundane users don't care about anyway), free archivers are often as good as commercial tools at compressing and decompressing files.