All right, this is the question that everyone usually asks and there are many different answers to it. I'm going to try and sum most of the answers into this one thread.
Tires are a HUGE mental game. I know this first hand because I used to only trust Michelins, and today I'm sponsored by Dunlop (Edit:1/1/16 Back to Michelins) Most of the time, any tire option will suit you just fine for street use (unless you try dirt tires on a street bike or something silly like that).
All major brands (Dunlop, Michelin, Pirelli,...) are great players in the game, so to say you like one brand better than the other because you like the shape of their logo doesn't quite fly.
First thing you have to ask is what do you want out of a tire? A race tire would be a waste of money if you're using your bike for street only. Even if your doing half street, half track, a race tire will destroy itself very quickly depending on your pace.
A street tire may not be suitable for any riders riding from mid "I"ntermediate group or higher. Tire just wasn't made for those kind of speeds.
Most tires available from your local vendor or a motorcycle website are street tires (ex.: Dunlop Q3, Michelin Pilot Powers, etc.). Race tires are usually a little harder to come by, you need to search them specifically or go through the manufacture directly.
However most people think that when they drop the bike is because they went in "too hot" and the tire lost grip, and that is simply not the case most of the time. Even with a stock suspension a motorcycle can do a lot more in a corner with a street tire. Most of the roads I've been to, I wouldn't even push the limit of the front end of my bike in a corner simply because the corner wouldn't allow me too (I'm sure there are roads out there that you can)
So when you go asking for "what tire is the best?" Or "what tire is better for my bike" remember that a lot of it has to do with your mind. Get what you think you would be comfortable with