A router/computer/IP address on the net is subjected to 4 scans per hour on average, and at peek times as much as around 15 times per hour.
Do we need protecting from these rogue access attempts? Actually, suprisingly 'not really'.
Most are opportunist wide scans looking for a particular vulnerability in your system and are scanning a wide range of IP addresses in the hope of finding somebody who is vulnerable.
Most vulnerabilities are patched out in OS updates or are only there because of virus' that have gotten out into the wild.
Protecting yourselves against these threats is quite easy, either install the latest Windows updates by A) Having a legitimate copy of windows or B) Having a copy of Windows sufficiently well hacked that you can run all the updates.
You might also try having some form of anti-virus protection, anti-virus software is a bit crap but some of them are at least not that intrusive on your system. I recommend AVG with a regular scan, you can set the scan settings to slow so that it doesnt interfere much with your computer.
Additionally those of us with a router already have the perfect hardware firewall and need no further protection from remote access attempts. Installing a software firewall in addition to your router will have the grand effect of protecting you from other computers in your house/network location, and prevent you from file sharing/printer sharing with your other PC's.
Routers are great because whilst all computers on the local side of them can go out to the internet and grab information, conversely anyone on the remote side of the router - should they attempt to port scan you - only reach the router which then doesnt know what computer to send the request too and discards it. Routers exceed software firewalls in all regards.
For best protection therefore:
* Run the latest Windows updates, or if on a Mac run the latest Apple updates, fix drive permissions, boot into single user mode and fsck -f, and hope your fonts are not corrupt.
* Run an anti-virus program regularly, if on Windows use AVG it's free and unobtrusive. If on a Mac dont bother most of the anti-virus tools for the Mac where on sale years before the first Mac virus appeared, does that tell you nothing?
* Use a hardware firewall (a router) and disable all software firewalls.