What can be damaged if I go a couple of months without getting my car aligned?

I have a G35 coupe and today had to get a new driver side front tire because the inside of it was worn down to the wire. They told me I needed to get an aligned check. Duh? So the driver side tire was worn down and the passenger side front tire knocks when I make hard-ish left turns. The car doesn't really pull in either direction. Oh and it's never been in a wreck. How long can I go w/o an alignment? And what exactly is it damaging while I don't get one? Thx!