Let's see. I switch back and forth between Panaracer Fire XC Pro 1.8's and some old WTB Racing Raptor 1.9's on a narrow set of rims. I switch back and forth between Ritchey Excavader Front/Elevader Rear 2.1's and WTB Velociraptor 2.1's on a second set of wider rims. Once I make a swap, the tires usually stay on until a situation comes along that simply demands a change.
The narrow Panaracers rule on narrow but generally smooth singletrack. They are light, fast, and hold a line very well. I'm suprised how well the front tire hooks up in the corners. They do better than expected in sand and mud but are clearly out of their element. At the preferred 55psi the rougher roads really start to hurt my ****. I save them for when I really need the extra speed.
The Racing Raptor semi-slicks were closeouts bought on a whim for riding the Moab Slickrock Trail. I run them anywhere from 45psi on slickrock up to 60psi on the road. They are good on the road and stick to sandstone, but on a lot of the local trails they can be downright scary. The front wheel and sometimes even the rear will just let go. They are worthless in the sand and mud. Being closeouts, they started to split from dry rot after the third or fourth ride. They'll be replaced soon enough, but I usually have them set up for commuting.
The Ritchey's are my newest tires at two months and they seem custom designed for most of our local trails. They are a skinnier 2.1 and are comfortable enough on the rough dirt roads and rocky trails at just under 50psi. They have a perfect balance of traction and weight they never seem to wash out in the loose gravel. Being 2.1's, I would expect them to be better in the sand, but the lower knob height just doesn't get the job done. They tend to pack up with mud too, but I live in the desert so that's rarely much of a problem.
The Velociraptors were what came stock on my hardtail. They are bigger 2.1's with giant blocky knobs and are pretty hefty at 700g each. These are my mudders and sandbox tires. In spite of the big knobs, I find I have to keep the pressure under 45psi or the front tire will just lose it on sandy hardpack. This makes them painfully slow on faster trails ridden with faster friends. After four years, they were starting to show their age when I picked up the Ritchey's. They are now kept in reserve for the occasional sand traps and mud bogs.
Each tire seems to have a terrain it was made for and a pressure it runs best at. Narrow tires are usually faster but less comfortable and more prone to snakebike. Wider tires tend to be more comfortable and offer more traction at the expense of speed. Lighter tires of a given size often lack taller knobs, have thinner treads and casings, or are a soft compound that sticks better but wears out quickly.
I consider having a quality set of tires that matches your riding style and the local terrain one of the best upgrades you can make. Avoid buying closeouts, many of these tires didn't sell for a reason. Once on the clearance rack, they've often been on the shelf long enough that dry rot is a distinct possiblity. I think tires are one place where you should just bite the bullet and pay close to retail.