The dining plan typically only saves money if you eat at the higher end restaurants and order the most expensive meals.
If you use your 1 table service meal at Splitsville and get a burger and a coke, your dining plan covers $20 worth of food, and you leave a $4 tip that you have to pay cash or charge to your room. However, if you use your 1 table service meal at Chef Mickey, your dining plan covers a buffet for $59.99, and you leave a $12 tip that you have to pay cash or charge to your room. Even if you get the "free" dining plan, you are now eating a $60 meal for "free", but end up paying $12 out of pocket. You could have eaten at Splitsville for $24 without the "free" dining plan.
If I don't buy the dining plan, I would be happy to spend $24 for dinner. Maximizing the benefit of the dining plan forces you to have more extravagant meals, and thus have a more enjoyable vacation. You are at disney to have fun, splitsville is not that different than a TGIFridays back at home. The disney dining plan keeps the character meal restaurants full.
I have 5 people in my family, if we eat at Chef Mickey, the DDP covers $300 for the meal, but I have to leave a $60 tip. If I go to Splitsville, my wife and I get hamburger and coke and my 3 kids split a $15 pizza and get 3 cokes. Our splitsville bill would be about $80 after tip. I am only spending $20 less for the entire meal than I did for the Chef Mickey tip, and I am sure paying a lot more than $20 for those 5 table service meals that we just used from the dining plan.
DDP for my family of 5 is $377.45 per day. I also get 5 quick service meals (~$60), 10 snacks (~$30) and 5 mugs (~$90) as well. If I back out the other items included in the DDP, I am paying about $197 for the 5 table service credits by purchasing the DDP. As long as my dinner for 5 before tip is greater than $197, then I make money. Chef Mickey is $300, so I save $103 if we eat at Chef Mickey (but have to pay $60 tip). Splitsville would cost my family $68 for a table service meal, so I lose $129 if we use the dining plan there (plus I have to pay $12 tip).
Because of the difficulty obtaining dining reservations, you could be in a situation where you pay for the dining plan, and the character meals and other higher end restaurants have no availability. In this situation, it may be impossible to save money with the DDP.
The dining plan also gives you "FREE" refillable mugs. I think these are $17.99 now to buy without the plan.
This site:
www.distripplanner.com has a nice tool that tells you if you should get dining plan or not based on the restaurants that you would like to visit.