In vim you can do that by putting these lines into ~/.vimrc:
map <up> <nop>
map <down> <nop>
map <left> <nop>
map <right> <nop>
imap <up> <nop>
imap <down> <nop>
imap <left> <nop>
imap <right> <nop>
This will disable the arrow keys in normal and insert mode.