Fortunately, the latest version of Google Toolbar for Firefox has a feature that lets you drag and drop files to your browser and they are automatically uploaded to Google Docs. To upload more files at a time, go to Windows Explorer or other file manager, select your files and drag them in Firefox.
To activate the feature, to go to Google Docs & Spreadsheets after installing the toolbar. You'll get a prompt that asks you if you want to enable the feature. Alternatively, click on Settings / Options and enable "Docs & Spreadsheets".
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Upload files using drag and drop in Firefox