Michelin Protek Cross Max. The toughest tire I've ever ridden. Never a puncture flat. I've picked out broken glass, small nails and tacks, bits of steel wire from radial tires, but nothing ever penetrated the puncture shield. The thick tread has been slashed down to where the yellow Aramid fiber puncture shield is visible, but nothing penetrated through to nick the tube. Possibly the perfect tire for bombed out roads and folks who are forced to ride the debris-strewn shoulders and gutters.
It's heavy but I use it only on one hybrid that I use for errands and casual rides. The tires don't feel sluggish on that bike, probably because I don't expect it to feel fast.
My other lighter, sportier hybrid wears Continental SpeedRides, a great all purpose tire with a minimal 1 mm thick puncture shield. It's had a few puncture flats, but not enough to worry about.
On my road bikes, I'd rather deal with an occasional flat than ride the lead filled garden hose known as Gatorskins. My only concession to practicality is I use Conti Ultra Sport II tires for everyday use. They're remarkably grippy, tough, durable, smooth rolling and resistant to punctures and cuts despite lacking any puncture shield. And at around $15 each, I don't even care if one gets cut to pieces. So far I'll wear them out from ordinary riding before they get enough nicks to do any damage. The last puncture flat I got was nearly two years ago.
I have a few somewhat better clincher tires: Schwalbe One V-Guards, Conti Grand Prix Classic, Vredestein Fortezza Tricomp. Occasionally I'll mount those when I feel like chasing a KOM or
PR. But they're a bit more fragile. One of the first Schwalbe Ones I got was cut to pieces long before the tread was close to being worn out.
If I wanted a puncture resistant tire for a road bike, I'd probably try a Michelin Protek Urban, or one of their tougher road bike tires like the
Pro 4 Grip Service Course. Based on my experience with the Protek Cross Max, the Aramid fiber shield seems to ride better than just slapping on extra thick rubber for puncture resistance -- which is pretty much what Schwalbe and Continental do for some tires.