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Actually, this is a common question, I find. The reason
why interviewers ask this is to ascertain whether you
are going to be hired out of the market quickly -- if you
are interviewing with other companies, your skills are
desired and it is in the company's best interest to make
a hiring decision immediately. If they wait too long you
will probably take another job. So, if I were you, I would
be flattered that they asked you this question.
Still, it is a little invasive to ask you the names of the
companies you have interviews with. However, the
interviewer was probably trying to assess which area
of the industry you are looking for work in. If you say
that you have two interviews with semiconductor
companies, one with an e-commerce software
developer, and one with a video game production
company, the interviewer will have a good idea of
where your talents lie, and who they are competing
against to hire you. This approach will save you from
revealing the names of the other companies or
sounding uncooperative.
Rather than be offended, be flattered. Be generous
and open with this information, and use these types
of questions to sell yourself -- "Yes, I am so good that
you need to make me an offer NOW."