That's a very disturbing question. I'd be torn between two responses:
I honor the contractual agreement with the social media sites I use not to divulge those credentials, just as I will honor the contractual agreement we make should you hire me. I don't give you my login credentials to their site anymore than I give them my login credentials to your network.
This is the best response. The requestor will have to admit that you are being asked to do something illegal if they push any further.
Thank you; I'd be sure to make the point that exactly the same contract law that governs the agreement between you and [Social Network] also governs the employment contract between you and [Potential Employer]. If you break the one when someone simply asks, isn't that an indication that you might also break the other if someone asks?
As a slightly more detailed reference to what Cadavre had already posted, here's the Facebook EULA
section 4 subsections 1, 8, and 9, which very specifically and explicitly prohibit allowing anyone else to access your account:
4 Registration and Account Security
1 You will not provide any false personal information on Facebook, or create an account for anyone other than yourself without permission.
8 You will not share your password (or in the case of developers, your secret key), let anyone else access your account, or do anything else that might jeopardize the security of your account.
9 You will not transfer your account (including any Page or application you administer) to anyone without first getting our written permission.
The LinkedIn EULA
has a similar section, also numbered 4:
4 Sign-In Credentials.
You agree to: (1) Keep your password secure and confidential; (2) not permit others to use your account; (3) refrain from using other Users’ accounts; (4) refrain from selling, trading, or otherwise transferring your LinkedIn account to another party; and (5) refrain from charging anyone for access to any portion of LinkedIn, or any information therein. Further, you are responsible for anything that happens through your account until you close down your account or prove that your account security was compromised due to no fault of your own. To close your account, please visit LinkedIn’s customer service site.
And on a purely security basis, I wouldn't type my password in on a machine they control, either.