Over the years the number of security flaws that come as standard with £50 plastic-box routers have been numerous. That 'free' router that came from your ISP probably suffers from one of these;
- UP & P enabled by default
- PING on the WAN side enabled
- Port 32764 left open
That last one is very serious as it allows a remote attacker to make a query of the router and dump out lots of diagnostic and configuration information. That may be of no consequence but it does allow a hacker to gain knowledge concerning your network and work on other attacks. The problem bedevils Linksys and Cisco models and SlashDot have a good write-up.
In a very real sense your router is the gateway between your network and the wild-west that is the public internet. If you can't even trust the little hardware device that sits in the cupboard under the stairs what can you do? Well, use an open source firmware in your router - Tomato is very user friendly and DD-WRT is very powerful. There are numerous others and since the source code is open it is regularly examined by the community that develops it and so many eyes spot any nasties (malicious or just bad programming) in the code.
I grabbed a couple of Buffalo models from eBay for when my eldest two went away to University and I wouldn't dream of letting my home network be based around a closed-source router.