It depends on who the composer is. For French music, Durand is usually considered to be the best, especially for more contemporary composers like Dutilleux. For Brahms, Schubert, Schumann, Beethoven, even Mozart (i.e. classical and romantic except Liszt and Chopin, and other less-known composers)...I think many musicians use Barenreiter and/or Breitkopf & Hartel...except for Beethoven's Concertis, for which Schirmer is actually the best (and the orchestration the most orchestrally satisfying by far). Barenreiters and Breitkopf & Hartels are rare in some markets (e.g. I barely see them in stock in Sydney, Australia), and Henle is thought of as the ubiquitous choice.
For Bach, some teachers do recommend that one look at more than one edition. Henle, while I think quite safe for students, is considered to be arrogant by many artists. For Chopin, it again depends on the teacher - there are some that purports the Paderewski edition absolutely, some that think it unreliable since edited by a pianist and not a musicologist (usually resorting to Henle), and even some that reverts to Mikuli's (which, to my personal taste, has some rather weird notes within chords)