For touring/commuting-Continental contact 37mm Hold up super well, I've got about 2500 miles on mine and they still look like new. Roll super fast at about 70psi, corner well grip well in the rain, etc

For cross all a-rounder/gravel/snow- maxis raze 33mm Not ultra lightweight but not a pig either. These grip well off road but have a near continuous center tread so they roll pretty quick. For mostly road rides I'll keep them at about 65 psi in the rear and 55 in front, if I know I'm going to be spending most of my time off road I like about 10-15psi lower in each tire.

For value vitoria zafiros 23-28mm They retail for $18 at the shop I work at, they have pretty good flat protection, roll pretty quick and once again are cheap. Not great in the rain, but again are cheap.

For road riding challenge parigi-roubaix 27mm. Not every road bike can take these but if possible they are awesome! I find they run best around 105-110psi in the rear and 95-100 in front. They corner great, are fairly lightweight, and roll very quickly.

These are just a few tires that I really dig, different situations require different tires.
One topic that isn't very exciting and doesn't get talked about much is tire pressure. I think that some of my favorite tires feel like crap with the wrong pressure. The maxis raze for example feels like crap if you go much over 70-75psi. I'd be interested to hear if people have specific pressures that they like to run, or if they just go to max psi like the majority of the riding public does.