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I'm asking this question from the perspective of someone who just wants to read journals rather than contribute to them. For the purpose of this question I'm using the definition of Open Access in the sense of the Budapest Open Assess Initiative:

"By 'open access' to this literature, we mean its free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, crawl them for indexing, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself. The only constraint on reproduction and distribution, and the only role for copyright in this domain, should be to give authors control over the integrity of their work and the right to be properly acknowledged and cited." (From the BOAI FAQ)

I'm aware of the mathematics journals listed in the Directory of Open Access Journals but I have no way of finding out from that list which journals are most respected by the community.

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    $\begingroup$ This is borderline for mathoverflow.net. We really only want "questions which can be answered", and the way this question is asked, it is likely to warrant discussion rather than definitive answers. That said, if someone wants to produce a table of eigenfactors for known Open Access journals, I'd vote that up. $\endgroup$
    – Kim Morrison
    Commented Oct 30, 2009 at 21:12
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    $\begingroup$ I may be in a minority, but I don't read journals, I read papers. If a paper I hear of is interesting or relevant, then I'll go and see where I can find it. If I may ask the OP, why do you want to know which ones are "most important"? $\endgroup$
    – Yemon Choi
    Commented Oct 30, 2009 at 22:01
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    $\begingroup$ I have to agree with Scott and Yemon. Not only is this a question that doesn't have an answer, I'm not even sure what the question is. What does "most important" mean. What kind of an answer are you looking for? I'm willing to reopen this question if it is edited to ask something specific. Perhaps what you really meant to ask is, "What are open-access journals I should know about? What distinguishes them from other journals? One journal per answer please. Vote up journals you really like (and leave a comment explaining why you like it, if possible)." $\endgroup$
    – Anton Geraschenko
    Commented Oct 30, 2009 at 23:10
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    $\begingroup$ @Anton - The question as written is exactly what I wanted to ask - it doesn't matter that I know about it, I want to know what the community respects. In composing it I used "Do good math jokes exist?", "Undergraduate Level Math Books" and "Most interesting mathematics mistake?" as models of what works well as a good mathoverflow question. I fail to see how they differ from the style of my question - are 'good' and 'interesting' less vague than 'important'? It would help if you could add some good vs. bad examples on the faq. As a community wiki it's ok that there's no answer to it (cf. faq). $\endgroup$
    – axiomsofchoice
    Commented Oct 31, 2009 at 12:12
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    $\begingroup$ IMHO, this question is interesting and should be reopened. $\endgroup$
    – Andreas Holmstrom
    Commented Oct 31, 2009 at 19:15

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