A crew of hackers (including hdm/metasploit, rezn, dinopio, drudge, kroo, pumpkin, davidc, dunham, and NerveGas) have introduced a one-touch instant jailbreak for both iPhone and iPod touch. The jailbreak opens your iPhone for full disk access and installs Installer.app so you can add pretty much any third party application you like.
To use it, open Safari and point your browser to jailbreakme.com (which we aren't linking to so folks won't install this by accident, but you are prompted to confirm). Once there, read the directions, scroll to the bottom, and tap Install AppSnapp. If Safari disappears and you return to the main Home screen, you're good. Just wait a minute more for your unit to restart--don't touch anything until you see the slide to unlock screen. If Safari hangs, just quit out (press and hold Home for 4-8 seconds) and try again.
Once you get to slide-to-unlock, go ahead and unlock your iPhone or iPod touch. You'll return to your home screen which will contain a new Installer.app icon. If you'll want to ssh into your unit, install the BSD subsystem, Community Sources, and then install Open SSH--you may need to upgrade Installer.app (thanks Ste). With Open SSH and sshfs (part of Mac Fuse), you can open Finder windows that offer direct drag and drop access to your phone or touch.
The jailbreak really is as easy as it sounds. I restored my iPod touch and jailbroke it just a few minutes ago and it worked great.
UPDATE: Please try to do this using WiFi rather than EDGE. Success rates are much higher!