When you want to add ringtones, change wallpaper, or run third-party applications on your iPhone, you need to perform a task called "jailbreaking". What this does is to open up your iPhone's file system so it can be accessed from your computer. There are a number of tools available to jailbreak.
If you're on an Intel Mac, you just won the lottery. The easiest software to use, by far, is iFuntastic. It walks you through the entire process with helpful prompts and pictures and is very simple to use. The iFuntastic crew promise PPC support in upcoming releases. If you are a PPC user and don't have the desire to download, compile and install complicated hacker tools you might be best served by just waiting for the next iFuntastic release.
Also keep in mind that you don't have to jailbreak on your own computer. You can borrow a friend's computer for 15 minutes to use iFuntastic. That's handy if you're a Windows users or on a G4 or G5.
A much more complicated alternative to iFuntastic is the iPhone Utility Client, with its amusing acronym iPHUC. You will have to google for the link as the website in question has requested no direct links. If you have access to developer tools, iPHUC will allow you to jailbreak on your G4 or G5. I warn you that the process is ugly and involves extreme hackery. If you want a slightly easier way to use iPHUC, the latest version of the iActivator tool performs iPHUC-compatible jailbreaks. Best of all, it's a Universal Binary.
For Windows users, there's the original fully-leaded jailbreak utility. The complicated bit is that it requires that you have a copy of the original 1.0.0 firmware present. To get that, you will have needed to have restored your iPhone at least once during it's 1.0.0 release.
The bottom line is that if you don't own an Intel Macintosh, the path to jailbreaking is difficult and complicated. You'll need to google a lot and, I recommend, rely on social networking. The best place to get started with jailbreak is over at irc.osx86.hu, in the #iphone channel. Be polite. And remember, anyone helping you out is doing so of their own goodwill.
Thanks Nate True, duck_tape and Ste.