If you are referring to Firefox 4, in that version you can drag the favicon at the left end of the location bar onto bookmarks toolbar to bookmark it. The favicon is also known as the site identity button

The drag-and-drop technique for moving an URL to a bookmark toolbar (and similar in-browser locations) or the desktop still works, but rather then selecting and then dragging the URL text, simply drag the "favicon" (icon to the left of the URL text) to the desired location instead. In other words, although selecting and dragging the URL no longer works, we can still create an Internet shortcut using the drag-and-drop method by dragging the favicon icon. For newbies: click on the rectangular image just to the left of the Internet address, hold the mouse button down, and while doing so, move the cursor until it is over the desired location, and then release the mouse button. This will create in your bookmarks toolbar or desktop (or wherever) a link to the webpage from which you dragged the Internet address.

Dragging an URL OR the 'favicon' does NOT work when you want to drag this to a sub 'folder' in your bookmarks. e.g. I drag an URL or favicon to Bookmarks, I have a sub-folder called 'Recipes' where I want to drop the dragged object. I position the mouse over 'Recipes' and the sub-menu appears. I move the dragged object to drop this on the recipe list in the sub-menu and the sub-menu simply disappears. Equally, I CAN drop this on the top level BM menu but it does not drop in the place needed (I want this (e.g.) NOT at the bottom but two up from there. What happens is that the dropped URL appears to locate it self in a random position. Easy to replicate by dragging the same URL to the BM menu and it drops wherever it feels like. FF team have clearly failed to do some basic testing on this and there are many (correction MANY) other annoying things like this that show there has been poor or insufficient testing. I have been a fan of FF for a long time and recommended it to others. Now I cannot do this with confidence and am seriously thinking of switching back to an old version. However, I might simply go to Chrome. Are you listening FF team? A simple look at the forums will show the groundswell of annoyed people. You have altered the way many things work, seemingly focusing on prettifying things rather than ensuring stability and ensuring basic features continue to work...

Maybe this extension from Alice0775 works:

• bug419911 (diagonal dragging): https://addons.mozilla.org/firefox/addon/bug419911-diagonal-dragging/
• https://addons.mozilla.org/en-US/firefox/user/84420/