I am applying for higher studies in US universities. Every time I fill up the online form, there is a section where they asked which other universities or programs I am applying too? Why do they ask these questions? Do they check where I am applying? What if I wrote a university name but later drop the idea to apply?
The questions referenced by GoodDeeds covers most of your question - the why. For the rest:
In the US it would probably be impossible (illegal) for one university to query another about a student's application, so, no, they don't check.
And there will be no consequences if you list a school and then change your mind.
Don't feel any special obligation to answer such a question. I actually doubt that they use such a question to determine whether to accept you or not. It could be counterproductive for everyone.