Are there math journals that are aimed for undergraduates? I don't mean here journals where students can publish their papers, but journals that publish introductory articles that an undergraduate can read without too much sweating, preferably when he gets bored or tired from his assignments and wants to read something different. What journals do you recommend to undergrads to read on a regular basis?

The American Mathematical Monthly. See also this list. 


As the name suggests, the College Mathematics Journal 


The mathematical intelligencer can be interesting. 


MAA's Mathematics Magazine is a reasonable expository journal. 


The journal "Morfismos" published by CINVESTAV, Mexico, is aimed at undergraduate and graduate students. Although some articles are in Spanish, they publish fairly good expository articles in English. For example, there is a survey on the recent solution of the Kervaire invariant one problem in this issue. 


Speaking of nonEnglish language publications, Сборник Математическое Просвещение is a terrific (and often overlooked) Russian journal, aimed primarily at undergraduates. 


If you read German, you can also try Elemente der Mathematik, which also have some articles in english. 


If you read German, you might also be interested in die Wurzel. 


The Harvard College Mathematics Review was another interesting venture, but it seems to be discontinued as of now. 


The MAA quarterly Math Horizons is explicitly aimed at undergraduates interested in mathematics. 


``Plus" an onlineonly British journal (similar to Math Horizons): http://plus.maths.org/content/ From their home page: ``Plus provides articles and podcasts on any aspect of mathematics, covering topics as diverse as art, medicine, cosmology and sport, a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers, reviews of popular maths books, and puzzles for you to sharpen your wits. We have a regular interview with someone in a mathsrelated career, showing the wide range of uses maths gets put to in the real world." The intended audience is not limited to math undergraduates; science undergrads would find something interesting there, too. Some articles can be accessible even to highschool students. And for those who read Polish, there is ``Delta" (which I used to read regularly in the paper version as an undergrad): The 01/2013 issue contains e.g. an article on William Thurston and geometrization conjecture (by Zdzislaw Pogoda). 


A journal similar to the American Mathematical Monthly, but in french, shall be launched by the SMF (french mathematical society) but I do not know when exactly nor what will be the title. 


There are two such journals published in India:



In the applied field there is SIAM Undergraduate Research Online. Although it is mainly for for research papers written by undergraduates they write that
An example is the paper "Moving Forward by Traveling in Circles" from the first volume. 


This one is nice: $\pi$ in the sky. 


If you understand french, "Quadrature" is also a good magazine which for instance contains sections about counter examples and history of mathematics. Recently a special issue about Poincaré has been published. 

