Obviously there's a princess, so I'm assuming there's a king/queen. Who rules the Toads and how?
The instruction booklet for Super Mario Bros. mentions a Mushroom King, Princess Peach/Toadstool's father, but he hasn't been heard of in many years.
In Super Mario RPG, Toadstool was assisted by the Chancellor, whose political function was about as vague as the Princess's. Paper Mario included a Toad Minister who looks and acts like the same person. These characters appear to have inspired the personage of Toadsworth, but he seems to function more as an attendant to the Princess than as a political advisor or executor. Mostly he accompanies Peach on her numerous vacations.
And it is telling that she takes so many vacations. Although Princess Peach lives in a castle, wears a crown, and is referred to as "ruling" the Mushroom Kingdom, she doesn't seem to wield any real political or administrative control, and we've yet to see a Toad Parliament or any such thing operating in her stead.
A parallel to Peach, Rosalina is a princess of sorts, wearing a crown, leading the Lumas as Peach does the Toads, and receiving as much devotion from her wards. But the Lumas don't call her "Princess"; they call her "Mama". They don't require laws or social services in their fairy-tale space-world. They're more like the Lost Boys crowding around Wendy, or Munchkins venerating the Good Witch Glinda.
Although Toads appear to enjoy more infrastructure than Lumas, and certainly have more need for protection from exterior threats, the same social contract seems to stand at the core of both societies: The Toads could theoretically take care of themselves, and for most practical purposes they do—but they're devoted to a nice lady upon whom they rely for emotional support.