What dietary practices are most helpful for reaching enlightenment? Gandhi, a Hindu ascetic, was adamant that the spiritual well being of a person was not disconnected from one's diet.  He said "The body was never meant to be treated as a refuse bin, holding all the foods that the palate demands."  Do the different sects of Buddhism have recommended dietary regimens?  If so, what are they?
In some of the Suttas in which the Buddha describes the gradual training leading to enlightenment there is the following stock passage:


  "Now, when a disciple of the noble ones is consummate in virtue in
  this way, guards the doors to his sense faculties in this way, knows
  moderation in eating in this way, is devoted to wakefulness in this
  way, is endowed with seven qualities in this way, and obtains at will
  — without trouble or difficulty — the four jhanas that constitute
  heightened awareness and a pleasant abiding in the here-&amp;-now in this
  way, then he is called a disciple of the noble ones who follows the
  practice for one in training, whose eggs are unspoiled, who is capable
  of breaking out, capable of awakening, capable of attaining the
  supreme rest from the yoke."


(Source: http://www.accesstoinsight.org/tipitaka/mn/mn.053.than.html)

This is explained in other places like so:


  "And how does a monk know moderation in eating? There is the case
  where a monk, considering it appropriately, takes his food not
  playfully, nor for intoxication, nor for putting on bulk, nor for
  beautification, but simply for the survival &amp; continuance of this
  body, for ending its afflictions, for the support of the holy life,
  thinking, 'I will destroy old feelings [of hunger] &amp; not create new
  feelings [from overeating]. Thus I will maintain myself, be blameless,
  &amp; live in comfort.' This is how a monk knows moderation in eating."


(Source: http://www.accesstoinsight.org/tipitaka/an/an04/an04.037.than.html)

As for Monks in the Theravada school, they only eat a single meal a day and do it before noon (although they are allowed to divide that meal into portions and have rice gruel before almsround). This kind of practice is also part of the 8 precepts that laypeople sometimes voluntarily undergo. The Buddha described the benefits of this practice here:


  I have heard that on one occasion the Blessed One was wandering on a
  tour of Kasi with a large community of monks. There he addressed the
  monks: "I abstain from the night-time meal.[1] As I am abstaining from
  the night-time meal, I sense next-to-no illness, next-to-no
  affliction, lightness, strength, &amp; a comfortable abiding. Come now.
  You too abstain from the night-time meal. As you are abstaining from
  the night-time meal, you, too, will sense next-to-no illness,
  next-to-no affliction, lightness, strength, &amp; a comfortable abiding."


(Source: http://www.accesstoinsight.org/tipitaka/mn/mn.070.than.html)

As can be seen, it isn't so much what you eat as how you relate to eating. If you eat with the attitude of caring for your health rather than for sheer pleasure, that will support your practice. Because this teaching is aimed at monks however, it is not required for a layperson to renounce eating food for the purpose of pleasure. It is only a recommended practice for laypeople.

On the subject of eating meat, the Buddha laid down three restrictions. In the Jivaka Sutta the Buddha said:


  "Jeevaka, those who say, that living things are killed on account of
  the recluse Gotama, and he partakes that knowing, because it was
  killed on account of him. They are not my words, and they blame me
  falsely. Jeevaka, I say that on three instances meat should not be
  partaken, when seen, heard or when there is a doubt. I say, that on
  these three instances meat should not be partaken. I say, that meat
  could be partaken on three instances, when not seen, not heard and
  when there is no doubt about it."


(Source: http://www.metta.lk/tipitaka/2Sutta-Pitaka/2Majjhima-Nikaya/Majjhima2/055-jivaka-e1.html) 

In this particular sutta the Buddha not only permitted meat, but rejected the idea that eating meat is inherently evil. This fits in with the Buddha's other teachings on morality that Karma goes by intention. The killing involved with meat is too far removed from the eating of it to automatically make eating meat morally wrong.

That doesn't mean that it is wrong to be a vegetarian however. If out of compassion one desires to support the welfare of animals by vegetarianism I think that is a beautiful thing. It is just something above and beyond what is morally required of a person.