There are several bathrooms in earthbound; however, every last one of them is occupied.

Now, we can applaud Earthbound for even including restrooms at all; most games don't even bother. However, one must wonder why they are always occupied, and where the people of Earthbound go to the bathroom if indeed the bathrooms are always occupied.

For the question of why the bathrooms are always occupied, it is a simple matter of the population to toilet ratio. As an example, we will consider the town of Onett. There are only two public restrooms in the town, both in the Library. (The jail cells may hold restrooms, but they aren't public). Given by the fact that knocking on the outer door of the restroom initiates the response that its occupied suggests that both of these are those tiny little single-toilet restrooms. There do not appear to be any bathrooms in any household that you can enter, and we are assuming that this trend continues for the houses we cannot enter. This means that there exactly two useable toilets in the city of Onett. For a family or two this may be reasonable, but we need to consider the population of Onett.

Assuming each house (except the house for sale) has one family each and each apartment has one family per floor except the apartments in the northwest which have about two per floor, I estimate there is room for about 26 families in the town and its northern suburbs. Just for the purposes of having some data to work with, we will use the US Census 2000 statistic of 2.59 persons per household; we discover that the population of Onett is approximately 145 people. Dividing by two toilets, we get that there are approximately 73 people per toilet in Onett. So, unless strict time restrictions are placed on use of the bathrooms, it makes sense that the bathroom is occupied almost constantly.

Okay, so we now know why the bathrooms are always in use, but we still don't know what the characters do for their toileting duties in the absence of an available bathroom. There are several possibilities:

The characters don't use the toilet at all
The characters just use their pants
The characters go outside somewhere

We will look at these one by one. First, there is the possibility that they don't use the toilet at all. This leads us to two subpossibilities: The characters do not use the toilet over the course of the game, or the characters do not have the ability/need to toilet at all. It does not seem likely that the characters would be able to hold off using the restroom for the entire length of the game as it seems that the game takes at least several weeks game time. As for being somewhat inhuman and not having the need to use the toilet at all, it seems that this is incorrect because if the characters in Earthbound did not have the need to use the toilet there wouldn't be bathrooms at all, much less occupied ones. So we can eliminate this possibility.

The second possibility is that they just perpetually wet their pants. Despite the popularity of this theory with clothing sellers, it does not seem likely for the following reason: Several characters mention wetting one's pants in the game, as if it's not a usual occurrence:

"You beat up the town bullies, punched them out big time, kicked their butts, bit their heads off, spit in their eyes, and made them wet their pants." -Mayor B.H. Pirkle.
"I'm so excited! I might just wet myself. My heart is going pitter
patter!" -Girl in Chaos Theater
"Jeff wets his bed sometimes. But other than that, he's a good boy." -Dr. Andonuts

So from this, we can conclude that using one's pants, while not unheard of, is not the usual occurrence.

This leads to the final conclusion that the characters must just go outside somewhere. This was even mentioned in Scaraba that Pokey "did his business" somewhere in the desert. So, the most likely situation is that the characters just wait till you're not looking and then go off behind a tree.