Lately my free AVG antivirus pops up with an annoying upgrade ad every so often. Is there any way to disable it?
No. You could either buy it or uninstall it. Any other ways (such as 'hacking' the application), if possible, are immoral and possibly illegal (depending on your country).
Although a lot of quality software is free, if you are the type of person who uses security suites, I strongly suggest you purchase and pay for it.
Some suggestions include:
Actually, the answer, well documented and easy to find now, is and always was "YES". Yes but you shouldn't is different from no you can't, so in response to joshhunt, you actually did not answer the question, and did indeed lecture. The OP could just have easily replied "they were immoral in abusing my trust, by activating a new hook on my 'free' software long after I agreed to the terms - that constraint being aggressive adware, operating far outside the bounds of the application's UI."
Regarding the legality of disabling the popups your free software emits, read your license agreement. I honestly don't know what the answer is, it cannot be assumed either way without reading that specific document, and I bailed on AVG when they assaulted my girlfriend with these ads while I was away (I wasn't even certain they were genuine at the time).
Regarding the morality, surely the reader doesn't need lectures from me.