gettin’ slick

Schwalbe makes several kevlar-lined puncture resistant tires. A couple of them are in high-volume 26″ size, and are generally slick compared to a knobby mountain bike tire. Note, though that they’re still high volume rather than low-profile road tires. They make low-profile racing tires, too, though I have no personal experience with them.

Their site is located here.

I switched over to their “Big Apple” line after my third flat on my rear tire in less than 500 miles, and I’ve had exactly one flat on that tire since (approximately 1,500 miles, most of it on the road).

Co-sign the schwalbes! You can buy them once, or you can buy some other tires 3-4 times.

Schwalbe are the way to go. I'm running the Marathon Tour Plus and have for several years now. Current set have over 10,000km on them without a puncture. Love them tires.

I like Specialized Fat Boys, despite the name, they are high pressure slick tires. They don't have quite the durability of the Schwalbes, but for $25, they don't have too.

Continental Town and Country tires meet your requirements and are easy to find.
http://www.performancebike.com/bikes/Product2_10052_10551

I also ride Schwalbes Marathon plus, >5K and no flats. However they weigh a ton, the ride is harsh BUT you get there. For an inexpensive tire with a nice ride I like Panracer Pasela TG. Comfortable, decent speed semi-flat resistant.
I have run the Schwalbes on less than ideal roads with good results. I can't say the same for the Paselas. So if your roads are good and your bankroll small get the Paselas.

The narrowest and highest pressure 26" slick I know of is the Hutchinson Top Slick,26×1, 130 psi.The Ritchey Tom Slick Pro is in the same category. The Michelin Wild n Run'R Light is very close to this 26×1.1 as is the Conti GatorSkin,26×1.125.
Any of these will give you a road bike like performance.
The next range is the 1.25-1.4 or 1.5",there are tons of choices here. We have a local criterium that includes a category for mountain bikes.They limit tire size to a minimum of at least 26×1.25 and no rigid forks, I race it on a Kenda Kwest which has a slight tread pattern, can be pumped up to 100 psi, and is available in 1.25 and 1.5 widths.
Tires bigger than this roll like pillows but provide a great deal of comfort and some off road capability.
I would spring for a kevlar beaded tire and remember that the lower profile tire combined with longer mountain bike cranks can lead to the pedal hitting the pavement if you corner with it down on the inside.