If you are wanting to use Safari, Apple is currently supporting Mac OS 10.5.x and 10.6.x. If your Mac can run 10.5, I would recommend upgrading by buying the DVD from a 3rd party retailer like MacMall or Mac-Pro.com as Apple Doesn't sell previous versions of the OS.
If you are using a 3rd party browser like, FireFox, you'll have to download the last build they put out before dropping support for PowerPC Macs this year.
mac 10.3.9 having trouble accessing Comcast.net getting a prompt to upgrade browser but already have the highest upgrd and i can not get through any Suggestions
You're seeing the prompt because your version of OS X only supports v. 4 of Safari. The broswer-sniffing code in comcast.net (and many other modern web pages) looks for minimum versions of web browsers in order to offer their customers the best experience possible on the web. When sites are forced to support old technology, it holds them back from what they are able to do. Kinda like driving a Shelby Mustang with one foot on the gas and the other on the brake. This is why websites encourage users of old web browsers (IE6, Safari 4, Firefox < 3.6, etc.) to upgrade; it enables site developers to take advantage of the latest technologies and give their customers a great web experience.