Here are the times we do not use "a" in English: when something is plural (ok, you know that :-)) and when something is uncountable for example: "She gave me perfume for my birthday.'' "The food needs oil." and many more. If you want to send me examples with and without "a" to explain. Please note that in Eng. we use "a/an" a lot more than in Greek.
jaye16, do you think that it would be acceptable to omit the article if we don't refer to the actual appliance but tv in general, similarly to when we say than someone works in tv? I mean, if I want to be able to watch tv programmes but I don't really care if I watch it on an actual tv appliance or on my laptop/phone or whatever, in this case could I say "I want to have tv"? If not, how would we phrase it, in order to make clear that we don't want the appliance but the ability to watch?