It's possible to insert posts by users through the front-end by using plugins such as gravity forms or by using wp_insert_post. However, how would one handle the editing of those posts? This has to be in a safe/foolproof/secure way for users.
What's the context or design purpose of the site? Is it a community with multiple authors or a team site? It might not be what you're looking for but you can enable users to post quick entries and replies, kind like a Twitter stream via the P2 theme. It is very, very simple but might work for you.