For people who just use computers sometimes, not so much, check the mails, visit a website, talk to some people on their faovourite IM, then they can probably live without an archiver.
But any serious computer user should have an archiver. They are very useful, it handy to be able to extract/compress files from/into many different archive formats. It saves disk space, saves bandwidth, can download/upload a compressed file/archive faster than uncompressed raw file.
You can send one archive containing thousand of files, instead of sending them one by one.
I use 7-Zip, I choose it because it is simplistic, light-weight, un-intrusive and because of its open and free nature.
There are probably alot of other decent archivers out there. Several years ago I used to use WinZip, it used to be pretty good. Now I dont use it anymore, because it sucks, I dislike it. It puts itself and runs in the background all the time instead of just staying away and not being there when not needed.