It depends, I would normally never give my personal information out to a company that didn't need it, if it's something legitimate like a bank where they're going to be managing your money long term then that's more understandable but these days I'm convinced that the only reason they want your information is to either sell it on the black market or keep it as a record so they'll be useful to government agencies. Many of the services I've used and seen could easily solve their record keeping problems by using a simple account ID generator and then just operate based on that, a lot of this information gathering is being done because of our governments being completely paranoid.
The reason I believe this is because me and my family have gotten so many mysterious phone calls ( some of them pretty damn creepy and stalkerish ) where they actually address you by second name despite never having contacted you before or worse yet some cunt in your earlier life somehow managed to get the information from an irresponsible school that doesn't respect your privacy and so on. I think like with self-defense the only people who are against anonymity have never experienced the need for it.
Anonymity and privacy are different things, I believe and hope, these companies that require some of my personal information will kept it private, and there are a few laws protecting privacy in EU, facebook got into a little trouble because of that.