How do I backup my iPhoto library to Dropbox or to an external disk?
Let me take a stab at actually answering the question.

First of all, do NOT use a FAT32 drive to back up your iPhoto library. The library frequently contains aliases/symlinks, and FAT doesn't support those, so they would either result in duplicate photos (in the best case) or break a bunch of your photos.

I don't think Dropbox has any limitation that would prevent it from backing up any/all normal files you'd store on Mac, which would include filename restrictions. Those would be a dealbreaker for any syncing cloud storage. So I think you can be confident there.

Dropbox seems to handle symlinks by turning them into duplicates. Other than that, people have been moving their libraries over to the Dropbox folder successfully. Here's a post to that effect – and in the comments are some common problems and solutions to this technique.

I've also (through a post on Apple's forums) found an app called Insync which utilises your Google Drive account. They claim to support symlinks … in fact a large part of the draw is that you can create symlinks to anywhere on your computer and direct them to the Insync folder (which then goes to Google Drive). In other words, you should be able to create a link to your iPhoto library and it will make a synced backup, rather than having to actually move the library to a synced folder.