Moodle
Since lockdown I have a new-found love for Moodle and its incredible versatility. When looking at other products, I kept finding things that I couldn't do, but in Moodle I could. With the new 4.0 version, it is now looking more modern and fresh (if you can convince your ICT to update your version that is...).
edmodo
edmodo is a fantastic free option for teachers and one I am considering using next year. You can set up classes, assign tasks and quizzes, keep track of progress, even add parent accounts. On top of this (which was enough to get me interested) it also has an in-built messaging system. An incredible amount of free features. 100% setup a free account and take a look.
Canvas
Canvas is an incredibly detailed LMS, and this video they have created is excellent, it covers many of the things canvas can do better than I would summarise here. So have a watch and get yourself a free account to see how you might use it in your teaching.
edapp
edapp (often previously shortened to just ed) is a little different from the other products so far. This is targeted more at mobile learning in micro-lessons, often advertised more towards industry than education, aiming at companies interested in upskilling employees. However, there are many nice features that lend well to the field of education, particularly the free template lessons.
Google
Classroom
Google classroom likely needs no introduction and I did not put it at the top of the page as plenty already know a lot about it. I would just point out that if you are a teacher you should be able to get google classroom for free (minus a few extras that institutions can pay for as part of the G-Suite). Take a look at the video to get a fairly comprehensive look at what google classroom offer.
Onenote + Teams
Similar to G-Classroom, most will have already heard of and maybe used Onenote/Teams. However, a lot of work recently has continually changed Onenote and in my opinion it could be the best on the market. My reason is mainly the ease in which students can draw/write freehand on a device with a digital pen. Literally like a digital exercise book.