According to EU sources, a Jedi does not have to take a padawan, and the rank of master can be achieved without taking one if the Council feels the individual's accomplishments and abilities warrant it. I believe the original Jorus C'baoth was an example of this.
And in ROTS Kenobi implies that the Council would some day soon make Anakin a master (and thus it isn't too important that he isn't made one upon his Council appointment), which would indicate that taking a padawan wasn't technically required. But this would seem to be the exceptional cases. The traditional path is to train a padawan to knighthood.