Big list of journals with free access to back issues. Now, I love it when I find a journal which allows free access to its back issues ! I propose to build a big list of such journals and I will start by putting down my own contributions.
 A: Recreational Mathematics


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*Ludus Opuscula RMM
This journal is very new. They allow access to all their articles on their websites.
A: Canadian Mathematical Society
I absolutely adore the CMS because of the amount of material they give out for free ! 


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*Crux Mathematicorum
This journal is dedicated solely to problem solving. It includes problems from Olympiads from around the world, a problem section where readers can propose problems and where solutions are published. It also has an excellent book-review section which never fails to inform me about excellent books I didn't know about before !


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*Canadian Mathematical Bulletin
This journal is dedicated to publishing short results and proofs. 


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*Canadian Journal of Mathematics
This is their flagship journal. 


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*Fibonacci Quarterly
This is not exactly produced by CMS, but they acknowledge CMS' help in their homepage. I have included it here for brevity' sake instead of making another answer. 
A: Nieuw Archief Voor Wiskunde from The Netherlands has been around for at least two decades, and I am sure it is still going strong. You can access the journal almost free of charge.
Asia Pacific Mathematical Newsletter is as good as the American Mathematical Monthly which has a problem section with very interesting and challenging problems that is also free to access.
