When you narrow a Finder window so much that it can’t display everything on the toolbar, the rightmost items get dumped into a menu that dangles off the right edge of the toolbar. If you’d rather keep the items at the right (the Search field, for instance) on the toolbar and let other things be dispatched into the menu, set them to remain visible in a shrinking window (this is a new feature in Snow Leopard).
Control-click on the toolbar item to get its contextual menu and choose Keep Item Visible.
Sometimes it’s a little difficult to get the contextual menu for the Search field to pop up—arguably the item that you’d most want to make permanent. Make sure you haven’t clicked in the field; if it’s active (framed in a blue halo), the contextual menu refers to the text that you have (or can) enter, and not to the field itself—unless you click right on the blue frame itself (a small target—it’s easier to open a new window!)
To reverse your decision, choose the command from the contextual menu again to uncheck it.