There are several ranges of dual-sport bikes on the market today, from the 250cc bikes that are mostly for off-road and just barely adequate for highway use, to the big BMW R 1200 GS that is considered one of the best long-distance touring bikes in the world, but (in my opinion) a little heavy for serious off-road work.
You need to decide how and where you are going to do most of your riding... If you want a street legal dirt bike, the Kawasaki KLX 250 or the KLR 650 are very popular. If you are looking for a mid-sized street bike that you can ride on a few back country trails, then bikes like the Suzuki V-Stroms or the BMW F-650-GS are quite nice. I believe BMW is also marketing an 800cc twin that is set up for light off-road use.
Of course, the ultimite dual sport motorcycle is still the BMW R-1200-GS, and if you get into the dealer's showroom at the right time of year, it may not be all that expensive... At least not any more $$$ than a new Harley-Davidson.
Whatever dual-sport bike you decide to buy, regular maintenance is the key to durability and reliability. Make sure you follow the manufacturer's recommended service schedule and inspect your bike for loose bolts and fittings on a regular basis.
Oh... Also, when you are shelling out the big bucks for a new motorcycle, don't forget to save a few dollars for a good quality helmet and appropriate riding clothes.
Ride Safe!