After some Googling, I found the solution in this article in the MozillaZine Knowledge Base: The secret is the browser.urlbar.maxRichResults key in the Firefox about:config screen.
To remove the auto-complete drop-down in Firefox 3, type about:config in the URL bar, then press Return. You may see a warning about how this may void your warranty; if so, click the "I'll be careful" button to proceed. In the search box on the screen that opens, type browser.urlbar.maxRichResults, then double-click on that entry when it appears. In the pop-up dialog, change the 12 to a 0, and click OK to banish the auto-complete drop-down.
To get the drop-down back, just change the 0 back to 12 (or whatever number you'd prefer).

