Over the years, while all other hindrances I can usually evade quite well -at least their grosser forms-, the hindrance of sleepiness/dullness is one I still have some troubles with as well. Because it's almost the direct opposite of mindfulness, it's hard to investigate it thoroughly. But I've learned about it quite a bit and this is only possible if you don't cut off your meditation even if you are sleepy.
It's not really that you are doing something wrong. This hindrance will be there until you are fully enlightened, that's the way it is. And even enlightened ones need sleep.
I've found out several reasons for it to occur:
#1 is the easiest, you are simply tired. Especially outside of a retreat setting, the mind is so active all of the time, it'll be sleepy and when it gets the chance, it'll go to sleep. This I found best to just sit out, just be tired, nod away a bit. Amazingly after such a meditation the mind can still be very peaceful, because you've made peace with it.
#2 is boredom with the breath. You don't find it interesting. If you can recognize this early on, you can evade the dullness just by seeing it. Other ways may be to change the attention to another body part, notice other sensations of breathing, change the breathing a bit etc. Everything to make it just a bit different.
That's my advice, but here is some advice that's probably better: http://www.youtube.com/watch?v=sB3cUVxfYBA