Science and Religion
When I was young and first learning guitar, I was often very impatient to be able to play just like my heroes. I had a fierce drive, and I wasn't afraid to bite off more than I could chew. This quality may have served me well in some ways (with The Little Engine That Could confidence), but it was also a major hindrance in other ways. I definitely had a tendency to try to run before I could walk.
For years (and to this day), technique has been a struggle for me. I think my over-eagerness as a beginner made me a sloppy player. When I was learning a new solo, I would often fluff over parts I couldn't play cleanly just to try to be able to play it up to tempo. I'd do the same when I was learning a new classical piece or even a pop tune. I remember when I first took lessons with Randall Dollahon at the University of Miami, he had me show him a list of standards I knew. I proudly produced a long list, and he asked me to play the melodies of several of the tunes. I couldn't get through most of them without making multiple mistakes (forgetting the bridge, etc...) and, in some cases, I realized that I'd never even bothered to learn the entire melody.
I've noticed that, when a musician has great technique, it's almost as much fun to watch him or her play as it is to listen. The movements of the hands of a master guitarist or pianist are beautiful and look almost like a miniature ballet: graceful, subtle, and effortless. In order to have excellent technique (or even decent technique), one needs to approach the instrument scientifically: patiently isolating each problem and slowly and methodically solving that problem before moving on to the next one.
On the other hand, we've all heard musicians who were technically brilliant but left us feeling rather cold. I think it's important to maintain a little of that youthful passion, and even impatience, in one's mindset in order to balance out the cold, practical "scientific" side. Mr. Spock needs his Dr. McCoy. Yin needs its Yang. The trick is to keep the two in harmony with each other so that one doesn't outweigh the other. Think of it as achieving a balance between the intellectual and the spiritual.
Hands in Harmony
Although your two hands are most physically responsible for producing music on a guitar, other parts of your body play an important role as well, and it's important to eliminate unnecessary tension from any part of your body while playing. Assuming one plays right-handed, the left hand is used for fretting notes, as well as for hammering on, pulling off, and effects such as vibrato and slides. The right hand is mainly the percussive element that actually strikes the string (except in the case of hammer-ons and pull-offs) and sets it to vibrate. Because the two hands have different functions, it's important to keep in mind that they should be able to work as independently of each other as possible. With the piano, both the right and left hands have the same task; both choose which notes to play, and both actually hit the keys to produce the sound. With the guitar, one has to divide these functions between two limbs just to produce one note.
It's the two hands that are directly responsible for getting sound from the guitar, and both hands should exert just as much pressure as necessary to produce the desired sound—no more and no less. Just as it's very common for guitarists to exert too much pressure on the left-hand fingers, especially for difficult passages, it's also common to compensate in the right hand and tense up there as well. As much as many players could stand to exert less pressure in the left hand, it is true that there are times when a considerable amount of pressure, and the resulting tension, is unavoidable in the left hand. The right hand, however, rarely requires that much pressure (either for pick or finger-style), and it can be useful to isolate the two hands and experiment with just how much pressure is really necessary to play a good loud rest stroke or fret an F barre chord so that none of the notes buzz.
Relaxation is even more important to keep in mind during technically-difficult passages. When things start to become stressful, our body's natural response is to tense up. The reason the great players look like they're playing effortlessly is that they are! I watched a video of a seminar that Lenny Breau gave in which he was talking about technique. He said that he always thought of a Zen saying he'd read once: "The easiest way of doing something is with the least amount of difficulty." Everyone laughed, but Breau said that this was essentially the encapsulation of playing with good technique.