In general, it's perfectly sensible to withhold information which might disadvantage you or be to the benefit of another party. This applies to salary conversations particularly.
However, when recruitment agencies ask who else you are interviewing with, it's often for your benefit. For example, in Ireland where I live, if 2 agencies submit the same CV to an organisation it is often (maybe always) discarded to avoid agencies disputing who presented the candidate - or both trying to claim fees - if the candidate is offered the role. Alternatively, they may want to avoid wasting your time by contacting you to suggest roles you have already applied for through other agencies.
You have to assume any agency worth their salt will be constantly monitoring job sites and cold calling potential employers to understand the way the local market looks. I think its unlikely they are hoping to mine your limited view on the current job market to fill out the bigger picture for them.
When an organisation has an in-house recruitment team, if they ask if you are interviewing elsewhere its often to understand how quickly they need to move if they want you. (This applies to agencies too I suppose so they can communicate this urgency to the client). For example, if you are actively looking, and at the later stages with another company, I will happily scramble to reschedule internal meetings so I can get you in for the next round as soon as possible. If, on the other hand you are being very selective about what you're applying for and don't have other irons in the fire, then I have a bit more time and I don't need to rush the department head back from a conference to meet you before somebody else snaps you up.