I realized that there are some old low-quality articles that I posted in my blogs. Is it okay to delete them or just let them be? What effect does deleting posts have in my blogs' seo, beneficial or otherwise?
Well if you get the PR on your pages or cached by google then I'm not saying to delete them if you are going to refresh your all the blog post and that pages are not relevant then you can delete
Maybe you could go over your old articles and re-write them to make them better? That way, you're keeping that particular url active, whilst providing the search engines with new content?
You can delete them, just make sure to 301 redirect that page back to your domain name or the catagory it resides in. This prevents you from losing any backlinks that post may have and passes the juice\value on properly.