Industrial application
The rare objection
The invention must be applicable within the industry, e.g. in agriculture. In the United States the invention must be useful.
It is very rare to receive an objection against industrial applicability since patent protection is something which is mostly pursued for inventions with a technical aspect.
However, you cannot obtain a patent for methods of medical treatment in Europe. On the other hand, patenting of devices and medicine used in treatment is accepted.
Exceptions
The US is fairly liberal with regard to the granting of patents. However, outside the US there are a number of exceptions to what you can patent. In Europe you cannot patent business methods, artistic creations, formulas and presentation of information as these in themselves are not considered inventions. Therefore, you cannot get a patent for the business method of buying quilts in China and selling them in Denmark, on a picture of the Queen, on realizing that E=mc^2 and on the contents of a telephone book.