I've always wanted to work with PNG-24 images on the web and not just because they offer greater compression and color depths compared to GIF but most importantly for their alpha-channel transparency and antialiased edges. In that way it's easy to create a single file that looks and works equally well on any background.
However I've stayed away and the main reason - up until Internet Explorer 7 there has been no native support for PNG alpha-channel transparency in its earlier versions.
If you don't care about IE6 users, it's fine - most modern browsers like Firefox, Safari and Opera(version 6+) fully support PNG transparency. Otherwise to keep those IE6 guys happy and treat them equally, you have to do a little more.
Or if you want to delve more into the subject:
Personally when I was building dimchevski.com I used Angus Turnbull's fix and got it running in minutes but now I think it's a little bit outdated and maybe a better workaround would be Drew McLellan's SuperSlight.
In any way you no longer have to worry as there are ways to make alpha-transparent PNGs work in Internet Explorer 6 and lower.