Today, File Sharing Service, Dropbox for Web has got Drag And Drop Support For File Uploading feature through Google Chrome, Mozilla Firefox and Safari. And bad luck of IE Users because they have not mentioned Internet Explorer in this list.
If you are using Dropbox for web for uploading, storing and sharing your files rather than it's Application, you can drag your files to browser window and it will start uploading. Dropbox team has included that:
Wanna see something awesome? If you use Chrome, Firefox, or Safari, you can now upload files by dragging them from your desktop onto the Dropbox website. After Dropbox detects the upload, it’ll work its magic to get your stuff wherever you need it. This is just a small step toward giving you a simpler (and more fun!) Dropbox.com.
So you can use this awesome feature to upload your files to Dropbox without installing Dropbox app Or Pressing the upload button. Just drag to store & Share. And no browser plugins or Add-Ons are required for using this Drag & Drop Feature.