Quite a lot.
For example have a look at this image:
See anything you recognise?
Not my code - I wish I were that talented. See
www.danasoft.com for how it was done.
The server has has to know you are "there" in some way in order to be able to send you the information you have requested, i.e. the code your browser will read to render the page on your display.
Now where "there" is is another question entirely, if you are really concerned about security there are all sorts of proxy services that can make you appear to be comming form somewhere that you are not.
As far as accessing your PC fro the outside goes, if you have a hardware firewall doing all the usual stuff, plus a software firewall (e.g. ZoneAlarm) - especailly if you are using a wireless network, run good up to date anti-virus / anti trojan software, are careful about unsolicited email attachments, don't install software you don't trust and are running all the latest patches for the operating system & all of your software you are probably as safe as you can expect to be and still have usable access.
To test your firewall have a look at:
https://www.grc.com/x/ne.dll?bh0bkyd2
and
http://www.grc.com/lt/leaktest.htm