You can sort journals by their submission fee requirement on the Directorate of Open Access Journal (DOAJ). I used this for years now and it been helpful to identify Journals with no submission or publication fees. I hope this helps.
You will find that most, if not all, journals that are not open access and published by the major publishers tend to be free for the author to publish in. Are you interested in a particular subject so I can give you some examples? Fees for authors are only common for open access journals, which are often called article processing fees. These are usually paid if your article is accepted.
Reputable journals do not usually charge authors to publish - at least not in my field. If a journal does suggest this it is probably not a good idea. If you 'google' the term 'predatory journals' you will get an idea of what I mean. I hope this is helpful.
Although there has been an increase in the number of journals requiring submission fees or other authors fees, as stated here in this discussion, payments are often not required by many traditional commercial publishers and university presses that are still using the reader subscription fee or individual article reader fee business model. There are directories of journals for different academic disciplines available, but some of those directories require a subscription to view. As Professor Griffith mentioned, it is usually necessary to examine each potential journal's website individually and see if there are fees required from authors for submission, processing, publication, editorial fees, subscription or other fees from the author. However, there are some publishers that state a required author fee, yet have policies for fee waivers that authors may be eligible for. Furthermore, it should be noted that not all journals that charge a publication fee are disreputable, and some legitimate outlets do charge fees. Authors need to be careful in using only the publication fee as a decision criterion. It has been stated by that there are relatively new journals that have what has been called a "conveniently quick outlet for a fee" yet are still reputable. It seems that the traditional publishing model is now encountering many challenges that are complicating matters for commercial publishers, authors/researchers, colleges/universities, funders/government, and society due to the many factors, including but not limited to, the internet and the open access movement. Interestingly, The Philosophical Transactions of the Royal Society that appeared in 1665 is commonly recognized as the first scientific journal. The journal as a form of research and knowledge communication occupied a needed space between the tradition of books and the exchange of written letters among scholars. This particular journal implemented a peer-review system in 1752 (Burnham 1990). Other scholarly societies then developed and supported journals from various science and social science disciplines, often maintained using subsidies and page charges to authors that could be argued as required by the value of publication as perceived by the societies and their members.
Burnham, J. C. (1990). "The Evolution of the Editorial Peer Review." Journal of the American Medical Association 263(10): 1323-1329
Most publishers' journals are free for authors if they are subscription journals. When sending an article to a Springer or Elsevier journals you are asked to transfer your copyrights to the publisher, but the publication is free of charge. This is not so with most open access journals where you can keep the copyrights to your paper, but you are asked to pay article processing fees.
You can sort journals by their submission fee requirement on the Directorate of Open Access Journal (DOAJ). I used this for years now and it been helpful to identify Journals with no submission or publication fees. I hope this helps.