Like most guitarists, the first way I learned to map out the fretboard was with the CAGED system. It uses five positions corresponding to each of the open major chords and is particularly well suited for playing pentatonic scales.
A few years ago, I abandoned the CAGED system in favor of the three note per string system. I arrived at the new system on my own, writing out fingerings for all sorts of scales and arpeggios. (I used to spend my college class time scribbling diagrams in my notes, then practice them later in my dorm room.) The system made so much sense that I knew it must have been in wide use even though I had never heard of it. Sure enough, a little Internet searching revealed that many others had been using it for ages.
The three note per string system uses seven different positions. The easiest way to map them out is with a major scale, starting on each of the seven notes. Just use three notes per string, and that's it. When you use a different scale, any notes altered from the major scale stay on the same string, shifting by the appropriate number of frets. Arpeggios are played just as they fit into the scale positions.
I see three advantages to using the three note per string system. The first is in scale sequences. Whether you're playing straight up and down the scale or jumping by thirds, all scale sequences in all positions will have the same picking pattern with slightly different fingerings.
The second advantage is in memorizing the positions. I found this surprisingly easy because each scale degree will always be in roughly the same spot, no matter what scale you use. For example, if a string has degrees 5, 6, and b7 for a Mixolydian scale, that same string will have degrees 5, b6, 7 for harmonic minor in the same position. I often refer to the positions by the strings where the roots fall (246, 135, 24, 136, 25, 146, 35) and build whatever I'm trying to play around that.
The third advantage I see is in the overlap of the positions. Any note on a specific string and fret, unless it's near the limits of the fretboard, will appear in three positions. The top two notes on each string in any position are shared with the position above, and the bottom two with the position below. This makes sliding between positions much easier.
A few months ago, I decided to switch back to the CAGED system. The three note per string system has its disadvantages too. Many fingerings require extra stretching. I had to stop playing more than once due to the beginnings of tendinitis. Also, pentatonic scales make perfect sense in the CAGED system and no sense in the three note per string system.
Since I've been using CAGED again, most exercises, especially arpeggios, have become much easier with less stretching. Until last week, I thought I had corrected my foolishness of neglecting the ease of one system for the logic of another. Then it hit me that I shouldn't be neglecting anything. Why stick to one system when I can use both?
Most experienced guitarists will tell you to learn both systems (see this lengthy discussion at Harmony Central), and I obviously did, but I thought I needed to pick one that best suited my playing. In a decision I should have made years ago, I'm now integrating both systems into my playing and my visualization of the fretboard. There will be even more overlap between twelve positions, and I can draw from a larger pool to find the best position for whatever I'm playing.
On top of this, I want to spend more time learning scales and arpeggios on single strings. This third perspective should help solidify my familiarity with the fretboard. And since I love sliding around, it should help with that again too.