After having my TortoiseGit shell icons stop working, I had to find the registry hack involved with deleting the 10 unwanted shell icons DropBox uses up. And the problem came back days later even though I'm pretty sure DropBox wasn't even running in the background. It seems to be a very long running annoyance that this behavior cannot be turned off in DropBox.
I only installed the Dropbox client because the web version is too glitchy, but if I'm going to have to fix this problem every week I'll just uninstall the client.