I heard of someone who just wrote at the top, “I just left the illegal questions blank, I hope that is OK.”
Brilliant! 
“If you have not served in any branch of the Armed Forces, state the reason why:”
The voices told me not to.
A subtle means of racism or a method to give Human Resources first dibs on the cute new employees?
I got nothin’ against them Viet Cong.
Not on a job application, but on a form to apply for a house rental.
Eye color?
We didn’t take the house and it remained empty for over a year.
I once filled an application that at the end, in the fine print, it stated that by filling out the application I was giving the company permission to do a credit check on me and that it would figure into whether or not they would hire me.
I didn’t turn it in.
Not necessarily inappropriate, but certainly odd; an application for a local government that asked for the dates of previous jobs, addresses, names of former supervisors, duties performed, and so on … for every job since entry into the workforce. This was for a job as a planner; not anything in public safety.
I called up the human resources department and asked for clarification. “You mean you want information for every job I have ever had, including things like summer jobs I had when I was in high school?” Yes, they wanted EVERYTHING.
My favorite is from the Staples application: How much did you steal from your last employer?
“As much as I could without being noticed” 
Clearly not enough, if I’m still looking to work at Staples.
Could that be a race thing? My college housing application asked for a photograph: turned out it was to determine race without stating as such (in the political climate at the time, it was probably to make sure no minorities were homeless).
I had the same thing happen to me when applying for a PA State job. I’m supposed to remember the name of my McDonald’s supervisor from when I was fifteen?
Odder still was the fact that they only gave you enough space to fill in information for three jobs!
A lot of companies just use generic forms without bothering to modify the information requested. Still, just to be safe, you could always answer that on “blue” regardless and see what happens.
You could always say that you performed your millitary service in a previous life.
Or, you wanted to join the millitary but they wouldn’t promise to let you “Nuke” anything.
Little Nemo, I like your answers.
Ohmigosh…you’re an Aquarius? Whoa. Whoa. I just don’t know how to deal with that. Give me some time…
I remember that question! Both my brother and I applied at Staples while in high school and I recall that after filling out that application he said that he had never felt like such a square before. The questions were phrased in such a bizzare manner. I don’t recall it exactly so I am paraphrasing here, but this was my favorite question:
Everyone has tried drugs at one time or another, when was the last time you got high?
“They asked. I told.”
Depends. You want me to adjust for inflation?
“I don’t think I want to work for someone with a history of illegal drug use.”
Correct response: “What time is it?”