How about through your categories and archives links? When an articles moves off the front page of your site, it is found within the categories and archives. Or if you are using a calendar, people can use that to find past posts, too.
See, we're not quite understanding what you want so we need specifics.
You want to display 3 or 8 articles on the front page of your site or in the sidebar. Do you want the whole post, excerpts, or just titles? Or do you want the first 1 - 3 articles to look one way, then a sign that says "these are the next five old articles"? You have to be specific as we are trying to help you.
I gave you instructions on how to make one page show up on the front page of your site. There is a plugin called customizable post listings that will allow you to list your posts in a variety of ways. With this plugin, you can list the most recent articles in your sidebar or below your most current post on the front page, or wherever you want it. I believe it will list titles and excerpts, but I'm not sure it will do the whole post, which is what you seem to not what anyway.
For very customized listing of information on your front page and throughout your site, read: http://codex.wordpress.org/The_Loop_In_Action
If you can tell us where and how you want this to work, then we can be more specific.
If you want to see an example of the many ways this can be done, check out one of my category pages on my site and move around the site to see if there is something that looks like what you want. I use the customized post listings plugin in several spots, and other tags to make post titles and post excerpts appear to help people find information. If you point to something specific, I'll give you specific help.