Yes, if you plan to stay in the US for keeps, it's a very good idea to get naturalized as Ian says. The downside is you cannot escape from the IRS if you do.
The US seems to be a bit ambivalent about the dual nationality thing. First of all, if you are a UK citizen, it's extremely difficult to give up your citizenship. There's even some chat (or used to be anyway) in a UK passport that says the UK understands that you may be obliged get a passport from another country, and not to worry about it.
I think Ian is right that you used to have to surrender a UK passport to the US if you became a US citizen (that is no longer the case) but according to a bloke I knew who had been UK/US for a long time, as the UK passport was the property of HM's gov, the US had to return it to the UK, whereupon, the UK sent it back to the owner with a nice note that said "you appear to have lost this".
I've always been a bit nervous about travelling with two passports and switching back to UK half-way across the Atlantic. There could be some collusion between the US and the UK and it might set off a few alarms. Paranoia on my part though. I have no evidence that anything like that happens.
Last year we were coming back from the UK via Iceland, and the immigration officer made some flip comment that we didn't sound like Americans. The red mist was rising in my eyes, but I managed to retain my composure. Then he made some comment that we had dual nationality. When his supervisor heard him say that, he barked out, "There is no such thing as dual nationality!"
Now here's a question. I was born in Scotland and if Scotland had installed an electrified fence along the border with England, would I qualify for a UK passport, a Scottish passport, both, or none of the above?