Honesty is the best policy.
The main reason the interviewers ask that question Are you interviewing with any other companies? is because they are interested in you and they want to figure out how much salary they should offer you. The other possible reasons are curiosity, job market survey, etc.
Had they been not somewhat interested in you, they would not bother(they have better things to do). They would finish the routine questions and say Nice to meet you. then let you go.
So, it's an indicator that they are somewhat interested, they want to know if you have or will have other offers.
Now, on your side, if you have not had any interview yet, just say so. It won't hurt you because you actually have nothing yet and you tell them you would be somewhat available. If you say yes you already have interviewed other companies, there would be two possibilities. One, they would make a better offer which is good for you. The other possibility is, they have budget concerns or they think you are good but not a perfect fit, they would rather wait and think about it. This would delay the hiring process. If I were you and if I want to work for that company, I want to go to work as soon as possible. Particularly if I am between jobs (unemployed), start my new job one week earlier means I earn 2% more salary this year. (I would make one more week pay.)
If you already have interviewed other companies or have scheduled interviews, give them the information. But, don't tell them what are the companies you have or will have interview with.
Honesty is the best policy. However, you don't have to tell them everything !