After searching the forum for a while I found out from this thread that Sublime's way of doing vertical selection is shift+right click and drag. Better than nothing, but I'd prefer to do it with my keyboard.
Other applications (at least Notepad++ and Word iirc) that support vertical selection use the shortcut alt+shift+up/down. This shortcut doesn't exist in Sublime, sadly.
I read through Default.sublime-keymap, but can't see any commands that appear to deal with vertical selections. Does this file include every single command support by Sublime, or is it possible there's a hidden command for this that I could use to create my own key binding? If not, may I request this be added to a future version?
Edit: Added "column" to the thread title to make it possible to find this thread if someone searches for column selection.