Archives are a useful navigation element for blogs that update daily and where posts bear a strong chronological reference. Prime examples of such sites are news/stock market related blogs, commentaries on daily soaps or webcomics with an ongoing story. The decision of whether or not an archive is needed can simply be made by answering oneself the simple question of whether or not a random user might be interested in finding out, what happened on the blog on a random day. When the answer is "no", then an archive is likely just distracting clutter and the space it occupies on the page could be used for better purposes.
Archives can be implemented in a variety of ways. The easiest one is to install the Views module and enable it's "archive" view, which provides a sidebar block, containing a monthly archive.