Quizzes with feedback are the main way I incorporate formative assessment into courses with regard to lower-level cognitive tasks; remembering, comprehending, applying, etc.
The Lesson Module is also built for this - there are branching options and a rudimentary adaptive lesson builder, such that certain answers lead students to particular pages based on their response.
Another less utilized tool is the Moodle workshop. I use this exclusively to provide peer-feedback and formative assessment on essays and presentations. It allows the teacher to collect files, distribute them to students, who then assess the work based on a common rubric. It then gives students grades both for their submission and for the quality of their assessment of others (as determined by a grading algorithm that is quite customizable) Of course, this is only for a rough draft, and for the process to be really "formative" you have to close the feedback loop by having those students complete a final draft after the workshop is complete. Be warned: this is a complex module with lots of settings (even more so than usual in Moodle) , so do your homework and a few test runs before deploying.
Forum is also a great place for formative assessment. If you deploy a forum with ratings in advance of a writing assignment or project, you can have students post and then give them feedback in the forum, along with ratings that aggregate in the gradebook if you so choose, and then correct their misunderstandings through replies. Grouped forums can be useful for this too - students in individual groups with the forum set to "separate groups" can have a private space in which to air questions and misconceptions before a grade is on the line.
Anyway, hope that helps! I'm a big fan a formative assessment and have had lots of success building courses around short iterative feedback loops like this.