You can currently expect op7, moz and iem to fully support alpha transparency images (PNGs). You can also get it in iew, but with some trickery. You can't get repeating backgrounds, for one. KDE said previously that they wouldn't add support for alpha transparency in konq because of the performance impact they would get from them, but that was a long time ago. Maybe it's changed. If not, expect Apple to add it in saf and give back to the community.
Mozilla also added support for CSS3-Color rgba and hsla through the extension values -moz-rgba() and -moz-hsla() not too long ago.
Also note that alpha transparency on anything that's not static has a terrible impact on performance. Have a few alpha transparency images bounce against the sides ot the browser window for awhile, and moz will run the speed of a snail who's had one too many trucks running it over.
What are some good PNG programs? I use Bmp2Png and PngCrush. With those, I made a 10 kb bmp file (200x24, 56 colors) down to about 100 bytes. Gif format could not make it less than 1 kb. Though the conversion programs I used don't seem to do any transparency effects, it did say something about it. But I don't know how to use it. Both are command-line DOS programs btw.
pngcrush, pngquant (this does alpha) and the GIMP (unless you want to pay for the graphics editor) are the tools to use. Photoshop makes really large and unwieldy pngs - I've even seen it produce pngs that are larger than the uncompressed png was.
Macromedia Fireworks is really, really good for pngs. pngcrush can seldom reduce file sizes that very much when Fireworks is the source.