Browser security question: how easy to hack remember password function?

I don't normally use this feature specifically for security reasons but am needing to use it right now some and am wondering if anyone knows how easy that is to hack if someone hacks into your computer. I don't mean random people hacking but a lot of my concern is the seemingly endless IPs from China that seem to enter random IPs all day (eventually hitting one) then trying to hack into your computer for unknown purposes. I used to keep track of this for a while (firewall logs) but stopped, but know its probably still happening, thus my question about security for "remembered passwords."