Many scholarly journals are Open Access, allowing the public to read their contents without subscriptions or university affiliations. The Directory of Open Access Journals is a good place to start.
Many academic databases are behind university logins and require an affiliation to access. The list of resources on this page are all available for free, open on the web.
Google Scholar is Google's version of an academic database with scholarly articles.
Try a live search here:
The resources below are provided by the Michigan eLibrary, and are free to use for any resident of Michigan. If any of these links don't work, please start directly at the MeL site here.
Outside of Michigan look for similar state-wide resources, like OhioLINK.