White shows blood best, which is practical on the mat. You want to know if you or your partner has a cut or scrape. However, women recommend keeping a black gi to train in during your period (1, 2).
Bleach is a non-factor because it weakens the fabric and will cause premature gi death by ripping. Blue and black look slightly more clean and sharp in more situations and for a little longer.
White is most traditional and connotes plainness or simplicity, whereas blue and black are "modern", if any of that matters to you. For instance, Roger Gracie won the BJJ Worlds a few years back in an unadorned white gi. The lack of patches, plus the fact that he submitted all of his opponents from mount, was taken as a message to the jiujitsu community. Some BJJ practitioners prefer the white gi for this reason.
IBJJF tournaments don't allow gi colors other than white, blue, and black:
The Gi should be completely white, royal blue or black. No Gi’s will be accepted with different colored jackets or pants nor will we allow the use of Gis with different colored collars.