What can I do to prevent cheating in my online classes?

Students cheating on online tests has nothing to do with Canvas or any other LMS platform specifically. The ability of the student to access the Internet during an exam has always been a problem and always will be. Here's a few articles on the subject to give you some background:

http://campustechnology.com/articles/2013/04/04/keeping-an-eye-on-cheaters.aspx?m=1
http://chronicle.com/article/Online-Classes-See-Cheating-Go/132093/?sid=wc&utm_source=wc&utm_medium=en
http://nation.time.com/2012/11/19/mooc-brigade-can-online-courses-keep-students-from-cheating/

The bottom line is that there is no magic bullet. Students have been cheating long before the Internet. Online cheating is just the latest incarnation. Based on the research we have performed, the following are some of the cheating prevention strategies instructors can use:

Avoid test-banks provided with textbooks. Many of those answers are widely available on the Internet.Randomize tests (questions and question order) as much as possible to prevent students from receiving the exact same exam (Canvas supports this)Alter assessments between class sessionsUse a mix of multiple choice and essay questions that require instructor moderation. Essay should be timed so that students will not have ample time to research online AND respond. They should only be given enough time to respond.Create questions that do not lend themselves to simple answers which can easily be ""Googled"". For example, questions that require an analysis of a scenario of your own custom design will not likely be found on the Internet in any easily searchable context. If in doubt - try searching for solutions to your own questions to ensure their resilience. Do not allow smartphones, tablets, or other devices during proctored exams.

Tools like the Respondus ""Lockdown Browser"" (which Canvas supports) can help with proctored exams but they are expensive and are not very effective with non-proctored exams since students can always just lookup answers on another device (smartphone, tablet, or another computer). That said, if the exam is proctored properly - there should be no need for a lockdown browser.

Consider online proctoring tools such as ProctorU (http://www.proctoru.com/forinstitutions.php). Students pay for this service separately.
Below are some additional resources for cheating prevention:

http://facdevblog.niu.edu/onlinecheating
http://www.westga.edu/~distance/ojdla/summer72/rowe72.html
http://www.na-businesspress.com/JHETP/BedfordWeb.pdf