1. Elsevier brands and markets a wide range of academic products. These include ScienceDirect, Scopus, Evolve, Knovel, Reaxys and ClinicalKey — and publish 3,245 journals and more than 33,000 book titles.
2. Springer (2,775) (Berlin based). From their website they indicate they publish more than 2,500 English language journals and more than 200 German language journals. If however you go Springer's 2015 Excel spreadsheet, there are 2,775 journals listed.
2016 Journals (including Open Access).
3. Wiley (2,339). Wiley Online Library. You will need a ScholarOne account for each journal to which you want to submit a paper.
4. Taylor & Francis Group (2,700 plus-Updated July 1, 2016). According to the T&F website, they now have over 2,700 journals. The list below are those that can be reached online.
5. Inderscience (413).
...and beneath these top publishers are many thousands more, 1,000 of which have made it onto the Beall List of Predatory Publishers.