Is there any websites that provide the DNA sequences of food samples?
I am not aware of any websites that provide full DNA sequences for food products specifically. In the context of your question, by "food samples" I am assuming you are chiefly referring to meat, fish, and dairy products (the headline-making categories of food fraud), although similar principles are applied to plant products, oils, rice, and other natural products.

PCR

There are a wide variety of genetic techniques used to detect food fraud or adulteration. These techniques do not look at the entire genome of the animal or plant from which it is derived – that would be extremely expensive and unnecessary. Instead, scientists look at particular parts of the genome that they know will likely help them distinguish one species from another.

This is where the primers come in. DNA primers are short segments of DNA that are used to initiate replication of segment of DNA, and is the vital component of PCR that determines which part of the genome will be amplified. Once the PCR product is amplified, it can be analysed by a variety of techniques. For instance, if the PCR products of various species are known, they can simply be run on gel electrophoresis which separates the DNA products by size. Thus if a band of an unexpected size appears on the gel you know there has been some contamination. There are also more automated methods of detecting fragment size via electrophoresis.

Examples of where these techniques has been used has been to detect:


cow's milk in buffalo mozzarella cheese (López-Calleja et al., 2004)
king bolete mushrooms potentially mislabelled as slippery jack mushrooms (Moor et al., 2002)
domestic pig meat in wild boar products (Conyers et al., 2012)


From the López-Calleja study on mozzarella, one of the gels looked like this: 



The PCR was run to detect cow's milk in buffalo cheese. Lane 1 corresponds to 100% cow's milk (it is a very bright band), lane 2 is 10% cow's milk, ranging down to lane 6 which has 0.1% cow's milk (a very faint band), and lane 7 is the pure buffalo cheese which shows no band. Therefore, this assay could be useful to rule out contamination with cow's milk.

Real-time PCR

Running gels is a somewhat old-fashioned way of doing things, and there are better ways to make use of PCR technologies on a larger scale. Real-time PCR is the technique now routinely done to detect food fraud. This is a variant of PCR, which (as the name suggests) allows one to quickly see which PCR products are being produced, in what quantity, and there is no need to run a gel.

For example, real-time PCR has been used to detect:


horse and donkey DNA in otherwise-labelled meat products (Chisholm et al., 2005)
pork adulteration in commercial beef burgers (Ali et al., 2011)
Atlantic cod, Atlantic salmon, and European plaice in fish products (Hird et al., 2012)
honey containing pollen from a specific region (Laube et al., 2010)


An example of what the read-out from the real-time PCR is given below. This example is from the Ali study on beef burger adulteration. The letter A was 100% adulterated (i.e. contained 100% pork instead of beef), letter B contained 10% pork, and so-on to E which contained 0.01% pork. F had no pork. The more pork contamination there was, the sooner on the plot (in PCR cycles) the contaminant reached detectable levels:



About the sequence

As you will see from reading about these techniques, it is not so much the sequence itself which is important – it is fragment size or other properties of the region analysed by PCR that is most practically useful. Sometimes the PCR product may be sequenced for comparison purposes, although I do not believe this is done as a routine screening for food fraud. 

Keep in mind that PCR is just one of a number of genetic techniques used in food safety. For example, DNA barcoding and SNPs are also useful techniques that are used in this field. The technology is constantly improving and evolving and no doubt more refined and efficient methods are being developed to detect food fraud.