Dropbox may seem like it doesn't need a lot of RAM to operate. The truth is: there's a lot of complexity under the hood!
For instance, Dropbox has to keep track of a lot of information about your files in order to make sure it can sync files quickly and efficiently. The more files you have in your Dropbox folder, the more memory Dropbox will need to keep track of them. That said, we are constantly working on making Dropbox more memory efficient and we continue to have significant improvements with each major release.
Want more details? Dropbox stores metadata on your files in RAM to prevent constant and expensive database lookups while syncing. The metadata includes paths to files in your Dropbox, checksums, modification times, etc. We are working hard on making this information more compact and are working on several fronts to improve memory usage. Our techniques are not limited to rewriting pieces of our source code and writing custom memory allocators.