Trouble with Trouble

Trouble has many definitions. Among other things it can be a state or a specific situation. So depending on what you mean either one could be correct. Check out the definition and examples:
http://dictionary.reference.com/search?q=trouble

The usage of trouble in the sentences used initially is correct. In the way you seem feel more comfortable saying it, the word problem might be better suited.

I don't think the word "trouble" should not be considered a countable noun. For different people and different situations, trouble can really be either one "thing" or many "things". I think that the word "trouble" encompasses all forms of ifself, therefore, does not need to be pluralized. Also, in the sentence "he gave me a lot of troubles", you have already espressed plurality in "a lot", so, "trouble" need not be pluralized.

"Troubles" would be used, then, as a verb. As in, "his behaviour troubles me." (A substitute for worry, I guess)

oops! I meant, i think the word should NOT be considered a countable noun.

sorry!

Maybe it would be easier if trouble wasn't a countable noun, but that's the way it goes. Both dictionaries and common usage treat it as such. The use of the plural just emphasises the fact that there are multiple troubles. I hope this doesn't cause you any troubles. :)

I've largely encountered it as a noun in the vernacular, not Standard English. There are, for instance, a few blues songs that will use phrases like, "Lord, I got troubles."

Don't forget double trouble!

I would say "I have trouble," if there's just the one. I would use "I have troubles" if my woman done left me, my mule done left me, and weevils ate the taters and I was therefore, in a sea of troubles.

Anonymous is correct.

trouble is a troubling word.

It is a word common in the African American vernacular (as so deftly captured by anonymous).

the "done" verb form seems to be an African-Americanism, or perhaps from the American south: it is an intensifier, or a signifier of permanence

My woman done left me

(my woman left, and she's not visiting her mother, she is not coming back EVER and dammit, it hurts.)