You could have a directory inside your main project folder that contains all the source code while the IDE 'project' files lie in the root folder. Just share the sub-folder via Dropbox, not the root one. This way each computer has its own instance of the project files.
Of course, as others have suggested, a real source code control system (repo) will make your life far better. The above scenario is accomplished by having the source code control 'ignore' the IDE project files (and any other junk files you don't want to share).
Most IDE's are aware of and designed to use a repo, so its pretty seamless.