Unknown to many hobby and amateur / semi-professional guitar players, fixing the intonation of an electric guitar is perhaps the second popular reason why your guitar sounds out of tune, besides tuning itself.
Even though you might have tuned your guitar to perfection, playing chords especially up the fretboard sound a little off. The problem usually seems to worsen, the higher up the fretboard you try to play.
The (possible) Solution
One of the really important, but usually neglected things when setting up a guitar of any kind, is checking its intonation. Basic tuning guarantees that a certain string played at fret #4 or #5 will sound the same as the string above it when played open. In other words, tuning sets up a relation between strings, so that one can then easily memorize and replay certain patterns across strings (chords and scales). What tuning does not guarantee, however, is whether the distance between every two frets is a perfect semitone (as it should be). This is dependent on many factors, but mostly, the thickness of each particular string, the curvature of the fretboard's surface, the length of the fretboard, and the distance between each string and the fretboard surface.
Regardless of the type of guitar, the fix usually lies in fixing the intonation of each string at the saddle. The saddle is the vertical plank at the bottom end of the guitar, which strings bend over. On acoustic guitars, it is usually a thin piece of wood or plastic, while most modern electric guitars ship with a separate saddle per string, which is mechanical and adjustable. Thus, it is usually much easier to adjust the intonation of an electric guitar. Acoustics will require fiddling with the saddle as well, which is usually something you'd like a guitar expert to do for you.
Fixing the intonation of an electric guitar boils down to measuring if the sound of an open string, and the sound of its harmonic, i.e. when the 12th fret of the same string is pressed, produce the same tone, but one octave apart. Despite years of ear training, you'd still want to to do this with a tuner, as often the difference might be less than a semitone (but close), and so difficult to discern. Usually, you'd tune a string as you do normally, check the intonation, tweak the saddle, redo the tuning, and check the intonation again, until you get assured that it is Ok.
Once you identify that the intonation needs fixing, it is important to determine whether the tone at the 12th fret is sharp ( a semitone higher) or flat (a semitone lower). In the case of a sharp intonation, you need to make the string longer, i.e. tighten the screw at the back of the saddle, so that the saddle moves further back. Respectively, if an intonation is flat, you need to shorten the string, by turning the screw to the left, and thus, moving it forward.
That's basically it. This simple tip helped me fix a brand new electric guitar, which was sounding way too off for its price. I hope it helps yours too.