When I started my project I was happy to use Groups in Xcode rather than literal folders: Since I'm using the browser in Xcode to access everything, stuff was nicely organized and I was happy.
However, now that the project is about to be shared for version control, the project folder itself is a horror show for those trying to scan it via a terminal, about 300 files, over half of which are graphics.
I'm trying to now reorganize things, creating real folders and importing them into Xcode. Unfortunately Xcode doesn't let me work with them the way it does with groups. For example, if I right-click on an actual added folder (blue, not yellow) and choose to add existing files, it doesn't actually put them in that folder, it puts them in its root.
Similarly, I can't move a file from a faux-folder (a group) into a real folder: Xcode doesn't consider the real folders to be valid places to move stuff to.
What am I missing? How can I convince Xcode to let me use the folders the way I use groups? There's an answer here to a somewhat similar question, but it doesn't actually solve my problem since I'm working with existing files.
FURTHER EDITED JUNE 2017: Xcode 9 does this automatically, no special effort required. This answer and Brandon's only apply to Xcode 8 and earlier.
EDITED DECEMBER 2016: Brandon's answer below is a better solution now. Back when this answer was created in 2010 this was the only option I could find. I now suggest Brandon's answer, below.
It turns out that moving files into real folders is certainly possible, though not as simple as it should be.
I got the basic information from a question here, Xcode organising files and folders (core data model objects - iPhone), but learned important things along the way.
Moving the files is a two-step process with multiple sub-steps:
Right/Control-click on the file or file group that you'd like to move and choose Get Info from the contextual menu that appears. The Group Info or File Info window appears.
Click the Choose button on the far right side of the window in the Path area. A dialog box appears.
Navigate to the folder you want the files to be moved to. Create a New Folder if needed. Click the Choose button in the bottom-right corner of the dialog box, then close the Group Info/File Info window.
The names of the file/files in the group will turn red to indicate that Xcode can't find them in the place you specified.
In the Finder (or Git) move the files you selected in step 1 into the actual folders you want them in.
Switch back to Xcode. The files/groups should all have turned black again. If any are still red then you've missed moving something to the right folder.
I learned a couple of important things while adjusting the ~300 files in this project:
Some files refuse to move this way; that is, when you navigate to the new destination the Choose button is disabled, as is the New Folder button. The solution, though I don't know why it makes a difference, is to first use Xcode to put those files in a Group (right/control-click the files and choose Group, and give the group a name) and then move the group to the new location. After you're actually moved the files in the Finder you can remove them from the group (by dragging them into the new parent group/folder and deleting the group).
Stop and build every few minutes, after completing step 2 for a number of files. The build will tell you if you've screwed anything up so far, making it easier to go back and fix it before you've done too much damage.
If the files won't move to where you want them to — I had a devil of a time moving some files that had been created early-on in the Classes folder — you can simply drag them out of their old place in the finder to someplace handy like the desktop, delete references to them in Xcode, and then re-import them via the right/control-click Add Existing Files option.
If in the past you've used Xcode to delete references to files without also moving them to the trash in this project, you'll find files that don't have to be moved but at just sitting there. Be careful that you don't do what I did, confusing the names of a current group of files I was moving and the older, no-longer-linked files, insisting that Xcode import them because you thought it was being dense.