I like Newcastle, and now I would like to brew some.
What class / style of beer is Newcastle?
Where does it get its brown color?
Are there any kits out there that would give pretty close results?
Newcastle is a Northern English Brown ale. It has a pale ale malt base with some caramel malts. It also has small amounts of darker malts like chocolate to provide color and the nutty flavor. They also use English hop varieties for bittering, flavor and aroma. It is drier, cleaner, less fruity, and slightly hoppier than the Southern English Brown.
Norther Brewer has their Nukey Brown Ale that is modeled after a Northern English Brown.
It's a Northern English Brown Ale, as Chris said.
One thing to be aware of that I have seen in a couple of clone recipes, including the one that's in BYO's special "Classic Clone Recipes" is that Newcastle is apparently a blend of two separately brewed beers. One is a stronger old ale, that is given a longer secondary fermentation before bottling. The other is a weaker brown ale that is brewed closer to bottling time.
Northern or Newcastle Brown as defined by the AHA Gravity: 1.045 - 0.050 IBU: 15 - 25 deep amber to reddish brown
Crystal Malt plays a big role in the color (typical English grain bill runs 15% of crystal and 2-3% of chocolate)
Get yourself a copy of "Designing Great Beers" http://www.amazon.com/Designing-Great-Beers-Ultimate-Brewing/dp/0937381500. Its got an outstanding section on Milds and Brown Ales, complete with grain bills. Granted it sounds like your shooting for extract, bu the history section alone with help with understanding your recipe formulation.
As others have said, Newcastle is a Norther English Brown Ale, and the color comes from caramel and roasted malts. The problem with cloning it is that the commercial beer is actually a blend of two beers after fermentation, so achieving the same flavors in one brew is difficult. I did find this recipe: http://www.homebrewtalk.com/f67/aberdeen-brown-ale-newcastle-clone-ag-36912/ which is modeled after the blending and basically uses a blended recipe instead of blending beers. I brewed a beer based on this recipe, and while my recipe is not a clone, the aroma is nearly identical, and the flavor is great.
That recipe does not include an Special B malt, which I'm nearly certain the original has, and is suggested in the comments in that thread. Also, that's an all grain recipe, and you wanted a kit (extract I assume), so I made one up for you at my LHBS, they have a great recipe creator. And this should be really freaking close in terms of clones.
As many others have said, its a Northern English Brown Ale. If you're interested in brewing one that tastes very similar, you can try Midwest Supplies "Old Castle" clone kit.