"Security"-pestering

This is bugging the hell out of me. You log into this web service, right, and what greets you? A screen asking you to do something you don't want to do in the name of security, and this doesn't go away until you do what they want, resulting in a sort of extortion scenario where you have to give in to their dubious proposition in order to be left alone.

These two haunt my web experience:

• Youtube wants me to link my gmail account with my youtube account for "security". There is no "Sod off, I don't want to."-button, just one that has it pestering me about it again the next time I log in.
• Facebook wants to know my cell phone number and another email address. For "security". Every time I log in, I get this screen. There doesn't seem to be any way of getting rid of it.

No, I'm not going to give in to their pestering. It's just going to drive me away from their services.