It's a little hard to figure, because there are so many ticket options and only you know which "extras" you may use, but the break even point on regular (non-"ultimate" or whatever they call it!) APs is around 8-9 days, as Gail Hayden said.
That being said, I have found that for me, personally, the biggest advantage of the AP is the park admission discount. Most of the time, when I call well in advance (6 mos) for AP discounted rooms, they are all gone, at least in the places I want. I don't think they put aside many rooms for AP discounts, especially in the value resorts. And not all of the restaurants give AP discounts -- in fact, it seems like about only 10% of the ones we go to give an AP discount. Since we don't buy souvernirs I have no idea if there are decent discounts there or not.
This is not to discourage you from buying APs! We bought one last year for each member of our family, and it is literally going to save us hundreds of dollars. We did a 10-day vacation last August, and we're going down for three-week s this July! It's just that if you're right on the break point and you're counting on the additional discounts over and above the park admission to make it worth your while, you may want to look very closely at the fine print.