It is very rare to find anywhere that you can submit your work unsolicited. As I have touched on numerous times the best and most consistent way to find an agent or get a contract from a publisher starts with a query letter. After that if they like what you sent them they will request more and ultimately may offer to represent or publish you.
There is an exception to this rule from time to time however and the current one I have found is from publisher HarperCollins, it is called the Wednesday Post. Here you have the ability to submit unsolicited work in hopes of gaining interest and a publishing contract. The submission still has guidelines of course and must be followed in order to move forward in the process but all entries meeting these requirements will be considered.
The guidelines state that an author must submit the first fifty pages or three chapters of their manuscript through the website. They do not want anything mailed or emailed to them. Along with the fifty pages they want a short synopsis and brief author biography. It is similar to the query in that regard but you can submit knowing that it will receive attention and if they are interested they will respond within four weeks.
Submitting can be terrifying and it is vital to make sure that your work is up to par when you prepare to do this. Just because they are accepting unsolicited work does not mean they want anything sloppy or unprofessional. There is a list of the genres they are currently looking for on the website as well as what they do not want. Make sure to read over the list before sending your work off to be considered. It is one more avenue open to lesser known authors to get our names out to a larger audience.