I don't look at any routinely. They are less significant in the internet age, especially at the cheaper end which tends to hinge around encouraging readers to buy more stuff. What I do look at, on and off, overlaps a bit with what Graham (
@myotis) chooses to.
I buy Hotshoe issues on an ad hoc basis when the content appeals - and as he noted, it's almost more of a book than a zine - but deeply rooted in the culture of photography. And I keep them like books - on my bookshelves, and long term. BJP was an excellent production that I would buy quite often from various newsagents, but has vanished from such retail shelves here at least - however over time I tended to chuck the issues I had out, anyway. The production was very good, but the format was too 'ziny'.
So it seems that the more it's like a book, the longer I'm likely to keep it.
'Source' (that Graham also spoke of) can be great fun. I've kept quite a few of those.
Odd that no-one's mentioned Aperture, or Foam ...
It could be said that overall, with magazines, there's a spectrum between the cultural & the commercial - and towards either extremity there will be increasing amounts of hype. So take your pick, or just don't bother.
If there's a crucial criterion, I feel that it should be to do with photography as culture (allowing of course for the mechanics & chemistry involved) rather than a cheap conspiracy that just wants people to buy more stuff.
The overall reference is that each of us is mortal - correct? Check. And that the planet we all live on & share is also 'mortal' - you want to argue? So where are we all headed? Let's keep perspective.
In the end, magazines are hardly in the mix. But for now, we're alive, & we do what we do ...