In the end, you're never safe. You can only protect yourself so much.
In fact, it is now a statistic that within 15 minutes of connecting to the internet your computer and home network will be scanned in one way or another.
So in effect, everyone is basically being scanned every 15 minutes by different random people, most likely looking for a target.
Basic scans will tell the person scanning that your computer is online, and if they take a more in-depth scan, they might see ports open of which they can manipulate to access your computer. By manipulate, I mean find a vulnerability in your system and hack your system.
I'm not trying to scare anyone, but it is the truth in the end. Everyone deserves to know. It only takes a maximum of 30 minutes to gain access to most average users computers. I'm pretty well bunkered in :)
Treat your horse the way you want him/her to treat you, then the eternal bond you share will be indefinately rewarding.