I have a website where only time email is sent is when user forgets password and needs to reset it. Can I use google apps to send this email via php on my site or would I be in violation of google terms?
I don't think it would be a violation if you're paying for Google Apps. If you have the free one, they limit you to 500 messages per day, and it may violate their terms.
You may want to read their guidelines here: http://support.google.com/mail/bin/answer.py?hl=en&answer=81126 or http://www.google.com/policies/terms/ or http://support.google.com/a/bin/answer.py?hl=en&answer=168383
You can use Gmail to do this as it's a perfectly normal use for email, taking a look at Google's guidelines for bulk mail senders might be a good idea.