Sometimes when typing, going into insert mode is a good thing. If I spell a word with one letter mistyped, I can hit insert and type the next letter and viola, it overwrites the mistake. Faster than positioning the cursor, hitting backspace or delete, then typing the new letter.

Also, CTRL+Insert = copy, Shift+Insert = paste. That sometimes works in places that CTRL+C and CTRL+V don't. It's also easy to hit those keys with your right hand. Depending on how you type, it can be faster to use your right hand for copy/pasting sometimes than using your left. Often I'll hold Shift with my left hand, use the arrow keys/page(up|down)/home/end with my right to highlight things, and copy/paste with my right since my hand's already right there.

EDIT: Added more reasons.