The iOS app is almost there. Once it has sync like the desktop (right now you have to individually download each!) and supports opening in GoodReader so there's good display and editing, it will be useful. But for now, if you want to do any practical device reading, you'll probably want to pull it down on the desktop and transfer into GoodReader via iTunes.
Even though you can store papers on Mendeley, I actually keep most of them on Dropbox.
Their priorities are a bit backward. The desktop app has been surpassed by almost all other competitors mentioned here. Sad. Used to be great.
I'm pretty happy with Papers, too, though I must second the other post about the Mac app being related to second class status. There has been basically no feature improvements (highlighting, for crying out loud) since 2008 when I started using it. Now I use Skim for annotating instead, which is a bit lame since you can't see the annotations within Papers, but the advantages outweigh the disadvantages.
I like to write company-confidential notes on the papers, so I don't sync them anywhere external, so as to comply with security guidelines.
That ends up meaning that 'sharing' papers means just emailing the PDFs around.
The git part somewhat laborious, but until SparkleShare gets released officially that's what I'll work with.
I should add that I arrived at Mendeley after Bibdesk, after Zotero.