The most reliable way to move your entire library to another machine is to copy the Zotero data folder from your Firefox profile on the first machine to the Firefox profile on your new machine.

To locate your Zotero data, open the Zotero preferences under the Actions (gear icon) menu and click “Show data directory” in the Advanced tab. In most cases, you will find your Zotero files here:

On a Mac:
/Users/<username>/Library/Application Support/Firefox/Profiles/<randomstring>/zotero

On Linux:
/home/<username>/.mozilla/firefox/<randomstring>.default/zotero

On Windows 2000/XP:
C:\Documents and Settings\<username>\Application Data\Mozilla\Firefox\Profiles\<randomstring>\zotero

On Windows Vista/7:
C:\Users\<User Name>\AppData\Roaming\Mozilla\Firefox\Profiles\<randomstring>\zotero

Be sure to close Firefox on both machines before copying the Zotero files.

In addition to the above method, you can also use a USB drive to sync your data between computers. Finally, Windows users can also transfer their entire Firefox profile with the tool MozBackup.

Users of Zotero 2.0 are able to automatically sync their library between multiple computers via the Zotero server. Note that files (attachments like PDFs, snapshots, etc) are not synced via the Zotero server. To also transfer your files, you can activate file syncing via WebDAV.

Exporting and importing your library (for instance via Zotero RDF) is not a recommended option. None of the available export formats allow for a complete transfer of your library data.