Is there a website that will know what news stories I like from what I normally read then only shows me stories it thinks I'll like?

Digg.com. There is an option to filter so over time the results reflect things you have shown intrest in, in the past.
You may need to be in the upcomming section to get this filter.

Try newsvine That’s the one I use. Just set up your account to show the items you want. The site can also be used as a blog, and a business or personal website.

All you need is cable.

If you are conservative, watch FOXNEWS.

If you are liberal, watch MSNBC.

If you are an independent, watch CNN.

If you’re like me, read the Onion and watch The Daily Show.

the news is just a big fucking joke anyway

@Blondesjon – what if you don’t live in the US and also want local news? ;-)

Anyway, Digg’s “recommended stories” works pretty well if you Digg a lot (say, 60 stories in 30 days), but I far from reach that lately. There was another website that tried the same a while ago, but I believe it has stopped and I don’t know the name anyway. I think Digg is your best/only option.

When I look on my Yahoo homepage, I have a button for “local” news and it gives me all the headlines from the local newspaper and TV stations.