Google Account

I could not get to youtube or mostly anything else on my computer, so I went to google and it said to fix this problem you can set up a free google account to help with this problem.  My questions is in all the years I have had my computer, I have never had that asked to set up an account with Google, I just always went to google and it would allow me to access Youtube and other website.  My question is, is there a fee for this even though it say free. and why do everytime me or my children have to sign in with my user name and password to just get into Google?