sometimes. things like "do you prefer to be the life of the party or watch things from a corner". unfortunately, there's nothing illegal in the usa about these employment screening tests (as far as i know - they have been in widespread use for years).
the catch with aspergers (and other handicaps) is that even if you can do the work, you're in the pool of job candidates with a lot of other people who can also do the work. you have to have something going for you that will make you stand out (in a good way) from the other folks who have applied for a job.
no, you can't be denied a job for having aspergers. however, unless you run into an incredibly stupid employer, nobody is going to tell you in writing that "you can't have this job because you have aspergers". and it'd be almost impossible for you to prove that it was the reason you didn't get the job. so you can quote the ADA, etc., all you want and it's pretty much wasted breath.
my suggestions for things that will improve your chances of getting hired:
1) get a skill that's in demand, that not a lot of people have. [i'm thinking that medical assisting and transcribing jobs are going to continue to be in high demand. you can get training certificate for those at most community colleges pretty cheaply. the medical coding, records, and transcribing jobs don't require a lot of people interaction. some of them can be done from your home. just a thought.]
2) get some experience - sometimes you can get around the "can't get a job to get experience because you've never had a job and so have no experience" thing by doing volunteer work or doing an unpaid internship. consider it an investment in your future. you get both experience and references if you do a good job.
3) it never hurts to know somebody who works where you want to work, or who works in the field in which you want to work. they can put in a good word for you with the people doing the selections. if you're looking at entry-level work, the first part of that is more important. if you're looking a little farther up the experience level, knowing other people in the field is a plus in addition to knowing someone in the organization.
4) think about going to work for the government. civil service jobs are based more on test scores and lists than personality tests. it also doesn't hurt to know someone in the government organization, but you have a better chance of getting hired, i think, here. the feds, in particular, have some good internship programs. again, the problem is that a lot of people are also going to be trying to do the same thing. so those qualified lists can be really long, but once your name comes up they will have to interview you and a couple of other people with the same scores. it helps your chances.
best of luck
PS one extra thing on the feds - if you are qualified by your state vocational rehab agency as having had a severe disability (and if you're pretty functional even with aspergers you probably won't be considered that disabled) there is a special hiring program with the feds that gets you, if hired, a two year sort of probationary appointment in which you can prove yourself and get some seniority. after that you have to bid for jobs just like anyone else, but you've had a "leg up" into the federal service.