The New York Journal of Mathematics is a nonprofit electronic journal, which posts papers openly online so that anyone can read them without any subscription fee. And of course (funny that this has to be noted) it does not require that authors pay for having their papers published. It exists simply for the benefit of mathematical research and the mathematical community. This is how journals should be. There are others like it: there is the BJMA in which I have published in once. See also the list of free online math journals here.
The NYJM is more than a community project – it is a good general math journal. How do I know? The same way I know that other good journals are good: first, I take a look at the editorial board, and I see that there are distinguished mathematicians among the editors (and most importantly for me, I check that there is an editor who is close to my field so he/she will know what to do with my submission); second, I check to see if mathematicians whom I know and highly respect have published there; third, just to be on the safe side, I can browse the index and see if any famous mathematicians which I have heard of have published there too; fourth, I check to see if the journal is on MathSciNet’s Citation Database Reference List (it is); after that I may or may not decide to submit (and this of course also depends on what my coauthor thinks), and if I submit I also get an impression of how professional, smooth and fast the publishing process is. My impression from my recent experience is that the publishing process in NYJM is as professional, smooth and fast as I could hope for.
Unfortunately, some committees which make decisions regarding tenure and promotion also need to decide if the journals in which candidates publish are good journals. There are several “bibliometrical” tools which help committees and administrators figure out if journals are any good. Here at BGU the tool usually used is something called ISI Web of Knowledge. Now guess what ISIWoK says about NYJM. Seriously, guess: do you think that ISIWoK says that NYJM is a good journal or an OK journal or a bad journal?
HA! Trick question! According to ISIWoK, the New York Journal of Math doesn’t exist. There is no such journal. Now, the NYJM has been coming out since 1994, so somebody at ISIWoK hasn’t been doing a very good job. Or maybe they have?
Well: luckily my university has decided to treat NYJM as a real journal (I am sorry to admit that I probably would not have published there otherwise). Unfortunately, there is still a way to go: my university still uses ISIWoK to count citations, so for this paper of mine there will be no data. I hope that this will change before I am up for promotion.
UPDATE February 5, 2013: Mark Steinberger commented below that NYJM is now covered by Thomson-Reuters Web of Science, and that this is retroactive to Volume 16 (2010).