What's a good digital Nikon SLR camera model for professional photography?

Nikon only has one pro model at the moment: the D2Xs. This model combines high speed (8 FPS) low res, and low speed high res (12.4 MP). With Canon, it's still two seperate models and other brands don't have anything over 3 FPS.
One step down, and you have the Nikon D200. I use this model myself. Let's see.... metal body with weather sealing, 5 FPS at 10 MP, a shutter rated for 100,000 actuations, more features than you can shake a stick at, and curently just $1400.
Another step down, and you have the D80. This model also has a 10 MP sensor and it has the same large viewfinder as the D200. It does 3 FPS, it has a slightly scaled down feature set, the AF is a bit less advanced, and it has a (rugged) plastic body with a shutter rated for 50,000 actuations. It's obviously not as good as the D200 for action photography but for just about everything else it's a great camera.
Below the D80 you have the recently discontinued D70s, the D50, and the new D40. There's also several old models (D100, D2H, etc.).
The D40 and D50 are a major step up from point & shoot cameras but might lack some features for pro applications. It depends on what you want to use it for. The D70s and up are widely used by pro wedding photographers, etc., and the D200 and D2Xs can be used for just about anything.
So Nikon has a great camera for just about every budget / requirement. The same goes for their lens selection.

Sorry, my response would be to look into Canon.

You might want to check out recent reports from the Consumer Report.

D50 and up...most have at least a D70 or D80.

I am just amplifying OMG's detailed answer, so vote him as the best. I own a D50 (my wife's), a D70s and a D200. ANY would be decent to start with, but the D200 is the one that is really "pro" level if you don't want to jump into the deep end with the D2Xs. I'd rather see you buy a D200 and some nice lenses than the D2Xs and have no money left for lenses.