I just thought of a quotation: "Its funny how people see others as themselves". Is it grammatically correct?
It's funny how people see others as themselves.
With the addition of an apostrophe, the sentence is correct.
However, I am not sure the sentence means what you (or the author) want it to mean.
As it is written, it states that people look at other people and they think those other people are them. So Alice looks at Bob and she thinks Bob is Alice.
More likely, what is meant is that people have a tendency to project their own (character) traits on the people around them; they think that other people are like themselves. So Alice looks at Bob and assumes Bob is like Alice.
This is a subtle, but important distinction; I would write the idea down as:
It's funny how people see others as they see themselves.