I have a dialog that includes file selection and it has a "Browse..." button. But it seems like it would be a good idea to provide some kind of drop target so that the user can use his/her favorite file browser to select a file (or files) and drag it onto my application.
Is there any standard practice for what to use as a drop target?
Is it a file icon of some sort? what would that look like?
Usually if a window accepts files for drag'n'drop - it just accepts them anywhere in the window.
If you have a list of files (listbox/view) or an just an text box that accepts a single file, those individual control windows could be the drop target rather than the entire window.
Normally there is no visual indication that a window accepts file drops. The only indication would be that you try it and you don't get the no-drop cursor when you drag across the window.
(Note: this is under MS Windows, other os window systems may have different standards)
As Ruddy said, I don't recall any standard icon for the drop idea. There is one for the no drop as shown in this image 
Otherwise I tend to like this kind of drop explanation; I find them pretty explicit.
In Safari (on the Mac, at least), a file-chooser form element (Consisting of a "Choose..." button and a field showing the chosen file's name) is also a drag-and-drop target. (Contrast with Firefox, which treats the whole window as a drag-and-drop target, and will replace the current page with the dropped item.)
Other places, I've seen an inset box, sometimes with a centered, grayed-out "Drag items here" text which disappears if anything is dragged in.
I tend to think that drop targets should be where the file "should land". That is, if I had a browse button and file path editbox, I'd make the path box the target. If I made a document editing application, I'd make the entire editing area the drop target (unless that would make an embedded object of course ... :-P who said these things are easy?)
So I'd say it depends on the application. But having a dedicated, separate target with no other purpose than to drop things on may not be the best solution, since it unneccessarily clutters the interface even for people who will never be interested in using the feature.