The latest edition of European Photography contains a survey of international photography magazines. The selection of 43 titles ranges from print media to freely available magazines online. The freely available publications are listed below. Of these, the only one I currently regularly look at is Lens Culture - distinguished by its inclusion of video interviews with photographers.
American Suburb X
Foam is an obvious omission from the list and while the online version does not live up to the splendidly produced print version, it is a useful alternative (I'm sorry we don't subscribe to the print). Like Foam, Foto Kvartāls also publishes a free version online using the issuu platform and is similarly ommitted from the European Photography list. Admittedly it is published in Latvian, but it does claim to have an international remit.
The Canadian Prefix Photo is also not listed (not online) and neither is the Edinburgh-based Portfolio (not online, but available in the library).
There must be others... Etudes Photographiques, Fotografia, Photography Quarterly. If you would like to recommend one, leave a comment or even better leave a review (I think reviews of non-English language titles would be particularly interesting).
For convenience, I'll also list the titles that you do have to pay for - are these necessarily the better ones? I have highlighted the ones we take in the library [the links take you to the magazine homepage, not the full-text of the publication].
European Photography* [available online via Library Search]
International Photography Magazines. European Photography v. 31 no. 87 (Summer 2010) p. 74-5.
Groll, M. Bloghopping. European Photography v. 29 no. 84 (Winter 2008/2009) p. 70-2
Trenkler, K. International Photography Festivals. European Photography v. 29 no. 84 (Winter 2008/2009) p. 76-7