There are two types of courses in Coursera- free and paid.
In case of the paid courses, you can go to the course and navigate to the "Buy Subscription" page and click on "audit the course". You can watch all the videos for free, but you don't get access to quizzes and programming assignments (you never know what a web search will turn up ;)) ⊕. You do not get a certificate by completing a course or completing all courses of a "Specialization".
In the case of a free course, you get access to all the videos, quizzes, and assignments. You don't get any kind of certificate. Instead of going to subscription page, you can just click "Enroll" and choose the no certification option.
There are some great courses in the free tier (videos + assignments, no certs) as well. Dan Boneh's Cryptography and Grossman's Programming Languages A, B, C come to mind. Also Model Thinking by Scott Page.
There were some great discussions on HN in the past. [0][1][2]
⊕ There are courses where duplicates of paid assignments and quizzes are provided under "Practice Assignment" as opposed to "Graded Assignment". Like Martin Odersky's Functional Programming Principles in Scala MOOC.
[0]: https://news.ycombinator.com/item?id=25245125
