What are the Orthodox Jewish dietary laws?

Answer

In fact, there is no unanimity amongst the orthodox Jewish sects as to what constitutes "Orthodox Jewish dietary law' Since the four major kosher certifying agencies could not agree, and there are currently over 900 certifying agencies, an organization, ACKO now known as AKO, was created to forge a unanimous position. When the constitutionality of New York's "kosher laws" was challenged, the argument by the supporters of the law to the US Supreme Court was that there was to be a consensus establishing what was in accordance with "orthodox Jewish dietary law". See Commack Self Service v Rubin USDC:EDNY, et al

Answer

Here are the main rules in a simplied format.

Note: Kosher laws do not appliy to non-Jews.

Mammals - must have a split hoof and be a ruminant (it must chew its cud).
Fish - must have fins and scales
Birds - the laws are complicated, but in general, they must not be a scavenger or predator, and must have a societal tradition as a food animal, such as most poultry
Insects - there are 50 species of kosher locusts, but the names are lost in translation, so most Jews consider insects unkosher
Reptiles and Amphibians - are not kosher
Blood - must be completely removed from mammals and birds
Meat and dairy cannot touch or be cooked or eaten together
Fish and vegetables cannot be cooked together, but may be eaten together
Animal products - only milk, eggs, and other animal products of a kosher animal are kosher.

Furthermore, there are complex laws about how the animal can be raised, slaughtered, and processed (including supervision of the processing), and what parts of the animal may be eaten.

Summary of unkosher animals eaten in societies where Jews live:
shellfish
catfish
shark
pork
rabbit
snake
alligator
Turtle
horsemeat

Animals that are not agreed upon by all Jewish authorities:
swordfish
sturgeon
ostrich
locusts (listed above)
Turkey (only disagreed upon by an extremely small minority of Jews)