"У меня есть" is used as STATEMENT of possession, belonging, or when referring to kinship. The word STATEMENT is important here.

Examples:
1. I have a car - У меня есть машина.
2. I have an iPOD - У меня есть iPOD.
3. I have a brother - У меня есть брат.

In colloquial speech, for the sake of fluency, есть is sometimes omitted. This happens in dialogues and this makes your answers more emotional.

Examples:
1. Ты один в семье? - Нет, у меня брат. = Are you the only child? No, I have a brother.
2. Ты на работу на метро ездишь? - Нет, у меня машина. = Do you get to work by subway? - No, I have a car.

There is also a case when you have to say something like: I came here by car, I can give you a ride.
In this case you wouldn't want to say "У меня есть машина" (this would be the statement that you possess a car and the relevant fact here is that at the moment you came by car, not that you have it as a belonging), but rather "У меня машина. Я могу вас подбросить."

In brief, есть in most cases indicates that the fact of possession is important, which is not relevant information in many cases.