A number of blogs are reporting that you have to change your Netflix plan today to avoid the price increase, but that's only true if your "Next Billing Date" (found under "Your Account") is September 1st. Netflix recommends that you change your plan 2 days in advance of your "Next Billing Date" to make sure the plan change goes into effect.
If you're quitting or taking a Netflix vacation you should also do it 2 days in advance of your "Next Billing Date" because Netflix doesn't offer a credit for unused days. You'll have 7 days to return any DVDs you have out or you will be billed for the discs.
Netflix will save your queue(s) for up to 2 years, but if you're going to change to the streaming-only plan you should back up (print) your DVD queue because you will not be able to access it.
Your price will only go up if you're on a combined DVD & streaming plan. If you're on a streaming-only or DVD-only plan you're all set.
Here's the official Netflix blog post about the price increase from July.
Special thanks to Kyle.