When what he says is interesting listen to it carefully and answer to his question.If what he says is boring say sorry it did not go into my head or you can say sorry can you say that again. If he is to repeat he will understand how boring it is.This will give him a chance to correct himself and say only things that are interesting. 

Exactly you don care about him he will not care about you, very soon.

If you have this problem with other people too you might want to have your hearing checked or discuss this attention deficit problem with your doctor. But if you have no issue in listening to other people it could just be that your boyfriend is boring.

Does this happen with others, or is it just your bf?  If it's just your bf, I don't know quite how to say this, but some people are just plain boring.  They don't know how to tell stories or even communicate without putting others to sleep.   I have an uncle like this and my aunt is really unhappy in the marriage.  She doesn't want to tell her kids she divorced him out of boredom, but I'm pretty sure she'll leave him once they're grown.  Even at the dinner table during holidays, when he starts talking, some of us find reasons to leave the table. 

Anyway, I don't know what to tell you.  It's not easy telling something they bore the socks off you, but if you want to stick with him,  you have to find a polite way to do that, lol.  It might help if you can think it through carefully and identify what specifically makes him hard to listen to.  Does he ramble or go off on tangents?  Does he include unnecessary details?  

A good relationship doesn't require you to have all of the same interests, but at the very least it should mean that a conversation involves both of you, not just him talking to himself while you only pretend to listen.  At the very least you should be trying to change the subject or at least alter it enough that you can take an active part.  And if you are bored and zoning out when he is telling you about events in his actual life, well, how would you feel if he did that to you?

Your real problem is that you are with a guy you don't respect and who utterly bores you. I am honestly wondering why.

Just tell him you would rather be talking about sex, that should cut out the boring crap.Or tell him to dance with you..

I think you need to be more assertive about changing the subject or telling him upfront when the topic is of no interest to you. This isn't rude. Good conversation means considering your audience, he should want you to be engaged and enjoy hearing more from you than rote sounds of acknowledgement. But he won't know you are bored unless you tell him.

But, if you two don't have much to talk about except what he likes and cares about, and the things he likes and cares about are tedious to you, then you two aren't compatible and need to break up.

Try to be more of an active listener.  However, it's hard to focus on what he's saying all the time and it's not the end of the world if you don't remember or hear everything he says.  Pseudo-listening is something we all do at times.

ask him.............................