Society without an article is the abstract concept of society:
Society as a whole needs to take responsibility for these problems
Society with an article refers to a particular organization
I keep my money in a building society
I am a member of the amateur dramatic society
Something is generally countable except for
- abstract concepts like peace and fairness
- activities like swimming
- substances that are infinitely divisible (water, sugar, leather, soap cheese, etc)
Note that you can still use a plural for something that is uncountable, to
indicate there are multiple types of it:
I tried several cheeses at the food fair (meaning several types of cheese)
Going back to your examples,
Society doesn't pay enough to old people.
This is society as an abstract concept.
The society doesn't pay enough to old people.
This would be a particular organization, for example a charity that helps old people.
Societies don't pay enough to old people
This could be either referring to several different organizations (for example charities) or different kinds of abstract society, for example in different countries.
I think that the first example has the intended meaning and the other two, while grammatically correct, probably do not have the intended meaning.
Best Answer
It is a matter of different English styles. "in hospital" is more likely BrE, while Americans say "in a/the hospital" instead. Following link sheds light on it.
http://ask.metafilter.com/228242/In-hospital-and-In-a-hospital
So to answer, it depends which style you are speaking.
Hope this would help.