Any chord can be played as a barre chord, although only a few shapes tend to get used often.
Eg, in key of C, the other common chords are F, G, Am, Dm, Em.
The most common barre shapes are "E" and "A" for majors and "Em" and "Am" for minors. Using these shapes, you get the C key chords at these frets:
1st & 13th fret = F; 3rd & 15th fret = G; 8th fret = C
(shapes above 12th fret don't seem to display with fret numbers.)
3rd & 15th fret = C; 8th fret = F; 10th fret = G
5th fret = Am; 10th fret = Dm; 12th fret = Em
5th fret = Dm; 7th fret = Em; 12th fret = Am
Key of G uses most of the same chords, except it has D and Bm instead of F and Dm.
As with any major chord, D can be played with either the E or A shape:
And Bm can be played with either the Am or Em shape:
This means you can usually play any chord sequence in a few areas of the neck without having to move too far up or down.
If you include other movable chord forms (some of them partial barres), you can usually play every chord within a space of 3 or 4 frets, in any position.
Look up the "C-A-G-E-D" system, which is based on 5 movable major chord shapes.