You can also open vim in split-screen mode, with the -O option:-
vim -O file1 [file2 ...]
To then turn on diff mode, you need to run the :diffthis command in each pane.
Another use-case scenario, is if you've already got one file open in vim, and you want to open and compare it against another. Then you can use the following vim commands:-
:vs otherfile (open otherfile in vertical split screen)
:diffthis (turn on diff mode in original file)
Ctrl+w l (swap to newly opened file)
:diffthis (turn on diff mode in opened file)
You can then turn off diff mode in each pane with the vim command :diffoff.
EDIT
And the other standard one that hasn't been mentioned:-
vim -d file1 [file2 ...]
This is equivalent to calling vimdiff directly.