Honestly speaking from personal experience,the only time I would bother to answer the question is I was applying for a job and I felt that selecting "employee referral" (provided I was referred by an employee :) ) might get me an interview or atleast get my resume in front of a recruiter.
That said,every additional field that you require the user the fill up is preventing them from actually signing up and reducing your conversion rate.
This article actually found that reducing the number of fields from 11 to 4 increased the conversion rate by 64 %. The results summary of that
- Number of forms submitted increased 140%
- Conversion ratio increased 120%
Here is another blog which highlights the impact of shorter forms on increased conversion rates
That said,with regards to the question you had raised about the "How did you find about us field",this article gives some input about what happened to their form when they got rid of it. To summarize their results :
Many years ago we had a client who was having the debate about whether
or not to include the ‘how did you hear about us?’ question on their
form. To solve it once and for all, they included a wacky choice in
the drop down— “billboard,” and although the client never ran a
billboard ad, this ended up being the most selected choice. Question
removed from form forever.