No one "needs" a dining plan

.
However, there is really no difference between solo and family with regards to the plans. It's all in how you wish to eat and what your ideal plan it while traveling.
There are 3 levels of the dining plans (the all-inclusive plans, Platinum and Premium fall under different categories), Quick-Service (QSDP), "Normal" (
DDP), and Deluxe (DxDDP). They offer different options and entitlements, and it's probably easier just to point you to the direction of the Restaurants-> Dining Plan subforum than detail them all out here.
With specific regards to solo traveling, again, it's all about whether a plan would fit your, well, plans. For me, I tend to do DxDDP, since it's what closely matches how I wish to dine at Disney. The fact that I happen to be solo helps in the sense that I don't have anyone else to worry about when schlepping from restaurant to restaurant, and I only have to take my own desires into account when planning it all, but that's more of a benefit of being solo than anything to do with the plans themselves.
Now, of course, the raw dollars saved will be less when solo than with others. For example, in Sept/Oct, I'm looking at saving roughly $200 in total over 9 nights. With a family of 4 and a similar itinerary, that number may jump upwards of $500! But, the percentages would remain roughly the same (~15% in my case).
My typical pattern is mostly a 1 credit lunch and a 2 credit dinner, though I do tend to leave off some entitlements and even have 4 unused credits this year. So long as I come out ahead enough to justify the plan, I don't worry all that much about extra stuff.