Birds having beaks makes sense--it's light weight.  Why do all turtles have beaks?  Weird genetic drift that got fixed?  Selective advantage?  Do they have some form of digestion that doesn't need as much chewing?

You guys are great!
LW

In all honesty, I don't know, but I can rule out some things and offer some possibilities.

The easy answer is that they evolved from animals that had beaks and had lost their teeth. Certainly the most primitive turtle fossil we have already has a beak, so it is no surprise that all other turtles do too. Though why they might have done so is a mystery.

Reptiles in general don't do a lot of chewing. They basically just bite things off and swallow them down. Crocodylians are not unusual for reptiles in that they do what is called inertial feeding, which means they basically throw their head back, tossing the food down their throats. So we can safely conclude that chewing was not a factor.

The loss of teeth in favor of a beak is not an uncommon occurrence. For example, the ornithomimids and oviraptors are two types of toothless dinosaurs, but in both groups the primitive members are toothed. Why they lost their teeth is not known.

Beaks can also occur with teeth. Stegosaurs and ceratopsians both had beaks and teeth, with no evidence of any reduction in teeth.

A possible answer is that most reptiles are fairly homodont. meaning that their teeth are all pretty much the same. One crocodile tooth looks pretty much like another. Beaks could be used therefore as a way of increasing "tooth" complexity. Reptiles don't have incisors like mammals. You might say they are at a disadvantage in trying to nip things off without sharp teeth in the front. Beaks provide an answer to this problem by providing a nice cutting surface at the front of the mouth. This is of course speculation.

The apparatus an animal uses for biting is an adaptation to that
animal's diet.  Beaks are sharp and can focus force generated by the
muscles into slicing, cutting and prising in a precise manner, so
ancestral beak users clearly found great advantage in having beaks.  The
great thing about turtle beaks is that they're very adaptable tools,
and there has been little pressure for them to change significantly over
time.  The inability to chew with a beak is obviously not a problem for
the turtles using them, probably because the beak is suited to biting
off pieces of a suitable size for swallowing.  If you look at
herbivorous lizards like iguanas, they have tiny, diamond-shaped and
relatively undifferentiated teeth (they're all the same) which are
perfect for biting off cookie-cutter sized pieces of leaf which don't
need further chewing before they can be swallowed.  Same principle.

Insectivorous
lizards, however, do tend to chew their prey more vigorously, often
because the insects are often large relative to the head, but crushing
and perforating with teeth serves two important purposes: first to kill
the insect so that it's easier to manipulate and swallow, and secondly
to allow stomach acids to penetrate the chitinous exoskeleton and digest
it more quickly and efficiently.

Crocodiles also chew certain
types of food, typically anything that's too large to be swallowed whole
- again, it ensures that it's dead and easier to swallow, and smashes
hard shell, breaks bones, and punctures skin and internal organs to aid
with digestion.  The teeth at the back of a crocodile's jaw are suited
for this purpose - flatter, more rounded to better resist crushing
forces near the jaw pivot.  Crocodile teeth may appear at first glance
to be pretty much the same, but there are a few different classes of
teeth that have distinct functions.

Adam is of course right about the chewing seen in reptiles. Thanks for the comments (I hadn't really thought about the back teeth of the crocs in quite that way, so thanks for pointing that out).
I should perhaps clarify what I was getting at. Reptiles in general don't do much more chewing than is necessary to break up the food into swallowable chunks. Beaks are really good at slicing things up so it is really no surprise to see them develop. Compare this say, a cow, that spends a lot of time chewing, far more so than is needed to just swallow the food. This is because mammals, and in particular mammalian herbivores (not so much the carnivores which typically wolf down their food), add digestive enzymes into their saliva which helps begin the digestive process even before the food hits the stomach. This is one reason why your parents always tell you to chew your food before swallowing, it aids digestion (although pleae correct me Adam, if I am wrong about the relative lack of salivary digestive enzymes in reptiles).

Reptiles can get away with the limited amount of chewing because they have slow metabolisms for the most part and the food has a much longer residency time in the gut than in mammals. Mammals have to eat so much that they really can't afford to take forever to digest their food, as opposed to the weeks that reptiles can take to digest their food. Crocidylians are especially good at this in that one can identify croc-eaten teeth because the enamel gets digested. Teeth going throug a mammal's gut pass right through with very little damage.

So, to your question, yes, turtles have a digestion that does not need the extensive chewing you might associate with many mammals, but they share this with the very toothy crocs, so it isn't an explanation for beaks without teeth.

All living turtles do indeed have beaks, but some of the fossil ones such as Odontochelys (whose name actually means toothed turtle!) show this is something that had not evolved with the very earliest turtles, but somewhere later down the line. You can see the teeth in the pictures at http://scienceblogs.com/pharyngula/2008/11/odontochelys_a_transitional_tu.php

What would be very interesting would be for someone to carry out similar experiments to those where they were able to grow teeth in the beaks/jaws of birds - despite birds having lost teeth for millions of years, much of the genetic and developmental machinery is still present and with a little tweaking of this they can be made to reappear!