How can I increase the size of the handles/keys in the Graph Editor? I'm fairly sure I've seen tutorial videos where the handles and keys are larger and therefore more visible, but I'm not finding anything about changing the size of them in docs or on forums.
You can find this option in the user preferences. Go to File > User Preferences > Themes > Graph Editor and modify Vertex Size and Vertex Handle Size to your needs.

You can see the changes immediately, so make sure you have a graph editor with active keys visible, when you tweak the values. And don't forget to save the user settings.