The three main positions for natural harmonics are at the fifth, seventh, and twelfth fret. Every string has a harmonic at the fifth fret, the seventh fret, and the twelfth fret. You've probably heard these in the intros to songs by Yes, Metallica, and many others. There are a lot of possibilities of patterns that you can play with these.
One cool thing you can do is alternate strings. So, what if I play the low string at the seventh fret, skip a string, then move to the twelfth fret and play the fourth string. Alright. You could do the same thing on the next set of strings. It creates a very harp-like effect. If I play those together I get this. If I play that all the way across the neck I get this. Sounds pretty cool. It can also go from this note to the next note seventh fret, the next note fifth fret, third string.
And those are just the main positions. You also have these hidden positions. You have harmonics on the fourth fret. They're a little harder to squeeze out, but you can get some cool sounds from that. And the third fret. Here's a little pattern using harmonics of the third fret and fifth fret. That's from a tune of mine called Path of Least Resistance.
Now, in addition to all these positions that we've just looked at we can go above the twelfth fret, and we have harmonics here at the seventeenth fret. A little harder to squeeze out, but they're there. And then the nineteenth fret. Those are the same as the seventh fret.
So, as you can see, harmonics can be found all over the neck. Be sure to have some fun with them, and check out some of the other lessons here that I've done on harmonics.