[chryuop]

Sublymomanl, if it helps think that even in English you use counter...just not 100% of the times.
Think about liquids like water, wine and so on. You can say you bought some water, but if you need to specify the quantity you need to use a counter such as: 2 bottles, 2 glasses, 1 liter...and so on. The difference is that in Japanese the counter is used 100% of the times you use a number.
Getting a complete list of counters for us students is, in my opinion, close to impossible since there are so many.

But about counters I have a question too for the native speakers or who knows Japanese.
つ can be considered a counter and works with the 訓読み, but for small numbers. What happens for bigger numbers? I mean, it is ok to say 一つの質問,
but what about 20, 32 or 40? I guess saying 試験には三十二つの質問があります would be considered a mistake. I was taught for small things that don't have a real counter I can use 個, but not sure if it works for abstract nouns too.