The official Documents Blog announced that offline access for Google Docs will gradually be rolled out. Back in January, after testing, it was not made available. But now, I have discovered that logging in with my non-Gmail Google account, the service is already active.
Using Google Gears, you can sync your files, but Google recommends using this service with caution on public computers such as those in Internet cafes.
Syncing appears to be ongoing; you can right-click a file and then choose "sync now." However, my files were not synced. Even without an internet connection, I was still able to edit files locally.
When editing files offline, you can see a reminder at the top of the screen.