Is it a good idea to validate API query string parameters?

My company is revisiting our API design and trying to decide whether to validate query string parameters. From my investigation it looks like most major APIs allow extra parameters and just ignore them, but I haven't been able to figure out why. It seems to me that validating parameters is the way to go since it prevents strange results when parameter names are misspelled. So I'm interested in any thoughts on why those APIs might behave the way they do, and any opinions about whether restricting parameters might be a good idea.