Personally I have several reasons for advocating Web accessibility. First of all an idealistic one:
I want everybody to be able to use the Web. I am not disabled (yet), so I can (and am often forced to) muddle through sites that are badly built, but a person with a disability may not be able to. Since it is possible to build sites that almost everybody can use, I don’t see why we shouldn’t.
Then a few reasons that some may call selfish:
I do not have any problems related to motor skills, but I have a really hard time using dropdown and flyout menus, especially hierarchical ones, as well as phony Flash or JavaScript scrollbar imitations. Accessible sites in general either do not contain such obstacles or provide ways around them.
Despite having no substantial eyesight problems, I find reading tiny text (below 11px is tiny to me), low contrast text, and reading any size high contrast, light-on-dark text to be very straining. A website designed with accessibility in mind is less likely to cause legibility problems for me.
I like being able to use my keyboard to navigate websites. Accessible sites are keyboard friendly since they do not force people to use a mouse.