What is a fast and modern OS for an old iBook G3?

Give Gentoo a shot. It's geared heavily towards customization and performance.

"Really fast on an iBook 500 dual USB was OpenBSD.

However, it's rather sparse. If you know what you're up to you will probably be able to make it work fine for you, but mostly we own Macs because they are not like a ""server"".

I think NetBSD would be better but never managed to install it, even though the iBooks are listed as compatible."

You may try Yellowdog linux (PPC redhead fork) as mentioned or even Apple's OS9. Classilla or iCab are nice browsers for OS9.

"OS X seems sluggish mostly because of the memory hungry nature of modern OS X applications. If you use applications ported to Cocoa from Linux, where throwing expansive hardware at performance issues is less standard practice, then you can find that the bare bones of OS X aren't as sluggish as you thought.

The key is to be ruthless in rejecting resource hogs: besides applications that are always spinning pizzas, look to eliminate applications that undermine overall performance, such as Mail (often wakes up and swaps its great bulk in), and programs with large resident size (look at output of ps). Some tips:

Using Emacs is probably the best first step you can take: you can use it instead of Terminal, Mail (you'll need to use postfix to deliver your mail to a local folder), as well as most other text editors.
Browser choice is the hard one. There are very lightweight X11 browsers, like Dillo, but they are not fully featured, and switching between X11 and Aqua isn't smooth. Camino is probably the nippiest fully-fledged browser, but given the nature of todays web, even that will seem sluggish on such hardware.
Try to use a text browser alongside a graphical browser (Emacs has a w3-mode for text browsing) and shut down the graphical browser from time to time.
The brutal truth is that the modern web browsing experience assumes you have more than 256M: Firefox on Ubuntu is snappier than Firefox on OS X, but even there, its not the best.
Switch off Spotlight!"