In most cases it must be valid until shortly after the application deadline. You can find the information for the TOEFL requirements on the university's webpages (FAQs). Or you can always ask the admission office.
What about Stanford? I am still waiting for my rejection (from GSB). Last year they sent it out one day after acceptances. First acceptance was posted on Friday... so I wonder if there is still hope.
Yeah, Princeton is my last hope (for a PhD in Political Science). I have one application left but for a PhD in Economics. However, I found a typo in my SOP (copied text from Word into LaTeX where an apostrophe got lost) and I didn't get into any other program so I don't think I've got a chance.
For sure. I mean we have people here (on gradcafe) who got into Stanford and other great schools. The chances are high that someone will decline the offer.