There were seven (https://www.reddit.com/r/SavedByTheBell/comments/1auizni/my_sbtb_the_new_class_journey/) in total. Technically, Seasons 6 and 7 were actually filmed all at once, so they'll count as just one big season here:

Season 1 (https://web.archive.org/web/20190124151326/http://www.savedbythebellreviewed.com/2014/07/09/the-new-class-season-1-recap/)

Season 2 (https://web.archive.org/web/20190124151326/http://www.savedbythebellreviewed.com/2015/01/07/the-new-class-season-2-recap/)

Season 3 (https://web.archive.org/web/20190124151326/http://www.savedbythebellreviewed.com/2015/07/08/the-new-class-season-3-recap/)

Season 4 (https://web.archive.org/web/20190124151326/http://www.savedbythebellreviewed.com/2016/01/06/the-new-class-season-4-recap/)

Season 5 (https://web.archive.org/web/20190124151326/http://www.savedbythebellreviewed.com/2016/07/06/the-new-class-season-5-recap/)

Seasons 6 & 7 (https://web.archive.org/web/20190124151326/http://www.savedbythebellreviewed.com/2017/01/04/the-new-class-seasons-6-7-recap/)