there is an internet cache, that's just browser history and can be cleared.
there is no way to store exactly what you've been doing online, on the local machine, (just think of the disk space it's take!).
the only way that you could look at the local history after you'd cleared the history would be using some disk forensic tools.
that's the same for any file that you've deleted though, not just web history.
if the government really wanted to know your every move online then they'd install a transparent proxy server (like I have in previous jobs when the boss wants to know what's going on online), and that can record all your online activities, i.e website URLs download etc complete with times and dates.
this proxy server would be installed at the ISP end of your network, not on your home network or your machine.