Foods Allowed on the Paleolithic (Paleo Diet, Caveman Diet)
Meats and Eggs
Meats (including seafood) and eggs are perhaps the most important components of the Paleolithic Diet. Ideally, the animals from which the eggs and meat come from are fed a natural (to the animal) organic diet. That is, chickens have access to greens, insects, etc, as well as grain. Cattle eat grass and other pasture greenery. Fish should come from the wild, or at least be fed what wild fish eat. In any case, meats should be free of breading of any kind. 
Loren Cordain (The Paleo Diet) believes we should seek out low-fat meat sources, while others disagree. His reasoning is that today's meats are much higher in saturated fat so we should seek out low fat meats and then supplement with fats from other sources.
Vegetables
Vegetables are encouraged, although some versions of the diet except green beans and peas as they are legumes. Some versions simply say that if it can't be eaten raw, don't eat it (though this doesn't mean that it must be eaten raw, only that it should be able to be eaten raw). Potatoes and other starchy tubers (e.g. cassava) is an area of varying opinions.
Fruits
Fruits are generally allowed. Some advise that people who need to lose weight should limit consumption of high sugar fruits, especially dried fruit and juices. Some say everyone should limit these.
Nuts and Seeds
Nuts and seeds are generally allowed, though Cordain suggests that those who want to lose weight limit them to four ounces per day. Note that peanuts are legumes and NOT allowed. Some don't allow cashews, since they can't be eaten raw. Unsweetened almond milk and coconut milk are often used as substitutes for dairy.
Oils
Though authors vary on recommended oils, basically the consensus seems to be that the oils from allowed plants are fine. Olive oil and nut oils including coconut oil are generally encouraged (Cordain recommends canola oil, but not coconut oil). Fish oil supplements are often recommended.
Beverages
No surprise that water is encouraged, and generally tea is considered to be fine. Beyond that, there is some variation as to advice about coffee and alcohol. Of course, sweet beverages (whether sweetened by sugars or artificial sweeteners) are pretty much out, though Cordain feels the occasionally diet beverage is probably OK.
FORBIDDEN FOODS
Refined Sugars
There is a long list of ingredients which are essentially "sugar". Some allow small amounts of honey or pure maple syrup - but this would have been a rare treat. 
Grains
Yes, there were wild grains, and a few roasted kernels have been found in ancient fires. But really - how much wild grain could have been collected at a time? Answer: not much. Corn is a grain. 
Starchy Tubers
This is actually an area of some disagreement. Some say none at all, some say no potatoes, but others are OK. In general, avoid: 
•	Potatoes 
•	Sweet potatoes 
•	Yams 
•	Cassava 
•	Manioc 
•	Some say beets
Legumes (Beans, Peas, Peanuts)
These are usually outlawed on the premise that most of them can't be eaten without cooking, and that legumes have a high content of lectins and other antinutrients. Research into lectins is in its infancy and not a lot is known about this with any certainty, but if you are interested, Loren Cordain's 2012 book, >The Paleo Answer: 7 Days to Lose Weight, Feel Great, Stay Young has a great section about what is known at the present time. 
Dairy Products
Early people did not eat dairy products before animals were domesticated. It has been pointed out that there has been adaptation to dairy products in some genetic lines, but most authors of this type of diet exclude eating dairy including milk, butter, cream, yogurt, ice cream, cheese, etc. Others say that butter (and to a lesser extent cream) don't have much lactose or casein and are probably OK on occasion. All would agree that if you are going to eat dairy, make sure the animals are grass-fed, and most would encourage people to seek out raw forms. 
Some Meats
Most processed meats (made with nitrites and additives) are not allowed by some, including hot dogs, bacon, sausage, and lunch meats, although sometimes more healthy forms of these can be found. Others say there is a difference between processed (e.g. hot dogs) and simply "cured" (e.g. bacon), and it's most important to know your sources. 
Oils
Definitely avoid the following: 
•	Corn oil 
•	Cottonseed oil 
•	Peanut oil 
•	Soybean oil (same as soy oil) 
•	Rice bran oil 
•	Wheat germ oil
This includes products, such as mayonnaise, which include these oils. 
Cordain has a long list of preferred oils in his book based on their ratio of Omega-6 to Omega-3 fatty acids. He also is down on tropical plant oils (coconut and palm) which have high levels of saturated fats. Other writers definitely include these tropical fats as fine to eat, or even encouraged. 
Salt
Most authors of this type of diet advocate at least being moderate with salt intake; some say cut down as much as possible. 
Other
Earlier paleo authors were negative on vinegar -- more recent thinking seems to be moderating on this.