I've just noticed that those two, which I have completely no use of, are part of the common package. This means I cannot remove them without removing everything. But I like all the other webapps, GMail, Docs and so on. I just don't want Amazon popping up in my launcher when I go there once a blue moon and not leaving until I turn Firefox off. Is there any way I can remove it without removing the rest?
The common package does not itself contain any software, only dependencies. Your only problem ist, that by removing the common package (which you apparently have to do, if you want to get rid of amazon) tghe package manager sees no need anymore to keep all other applications. Because it considered them just a nasty dependency of common in the first place.
You can safely mark the commons package for removal and mark all packages you want to keep for installation. Depending on the package manager you use, you can do this in one step, before executing the change, so the packaging system will not remove, redownload and reinstall any software. It will just keep everything you marked for ... keeping.
As discussed in the comments to the previous answer (by Paul Hänsch), the Amazon webapp is part of 'unity-webapps-common', and all the other 'unity-webapps-*' depend on 'unity-webapps-common', so at this time there is no way to remove the Amazon webapp without removing the rest.
However, I just discovered a way to disable the Amazon webapp, without uninstalling it, so you can leave other webapps installed and not be bothered by the Amazon webapp.
I found these instructions here: