This is a very soft question, but it is somewhat relevant to some other questions, like Which are the best mathematics journals, and what are the differences between them?.
I've read that Notices AMS provides annual (at least) stats on backlogs, turn-around times and so on (when is this, by the way – is it the same month each year? And where is it? The faultless google has let me down ;_;) But what are some of the quickest journals? That being said, one has to balance speed with length of allowed papers (having a page limit of 15 sure would help speed up refereeing times, or am I optimistic?), general reputation and level of specialisation.
What is the quickest journal you are aware of for 'general' papers? For papers in your special field?
Alternatively, what about (unreasonably?) slow turnaround? I'm not asking for anecdotes, but documented evidence (Edit: perhaps documented evidence is too strong. I just don't want 'My paper took 3 years because it sat in someone's spam filter and then got lost and then the referee forgot about it'. If you have anecdotal evidence, then it should be either 'common knowledge' or at least corroborated by people you know). If this slow journal is because it accepts top-level research papers that are over 100 pages in length, then please say so.
Best Answer
International Math Research Notices is a journal that accepts `general' papers and has a reputation for turning papers around quickly. It is in fact part of their mission statement to do so.