I've seen people on the internet claim that you shouldn't tilt back your head during nosebleeds, because blood could get into your lungs or stomach. When I asked people I know what they do during nosebleeds and what they know, most of them tilt their heads back and put cotton tampons or handkerchiefs in the nostrils. None of them have suffered any trauma caused by swallowing blood, and as far as I know, it's rare for seriously bad effects to occur like this.
There is an infamous photo of a very large branching blood clot (http://www.snopes.com/photos/medical/bloodclot.asp) which is used to scare kids about nosebleeds, but it seems to be an exceptionally rare occurrence. At least that's so uncommon that I've only seen that in this one picture.
One common thought that goes through minds of people I've talked to seems to be "Blood loss is a thing, and I'm losing blood, so I better swallow it back into myself".
I'd like to ask the more knowledgeable folk on this site: Is swallowing own blood from nosebleeds harmful, neutral or beneficial?
I've found a question on SE about consuming blood in general, and the recommendation is against that, but in that case it's extra blood that wasn't in your own body's circulation. So this is a different question, just in case.