We are deploying a web application and I am considering replacing some of the JPEG graphics with PNG.
Has the use of PNG-aware browsers passed 95%?
IE has had PNG support since at least IE4, the Mozilla suite had it back before Firefox came around. Opera, minority player that it is, has had it for about as long. Netscape 4.7 I think does not. So I'm pretty sure we're over 97% right now. At least, on my web-sites.
I don't know anything about mobile/phone browsers, though.
All the newer versions (and older versions of many) of the major players support it. Something you'll want to look for is full Alpha and transparency support. There are hacks you have to perform to get even major browsers to recognize these, some times it's just not possible.
Check here for a listing of png support status in browsers, major and minor.
With regards to the use of PNG, it's gaining popularity but I don't have any numbers of how big of a "marketshare" it has. I personally make my decision based on browser support.