Why help them?
A legacy of colonialism, the Commonwealth and a sense of moral duty for one, and if not, perhaps more practical options like helping them is economically benificial to all, it brings them out of poverty, and will help avoid resentment and curb extremism: economic developement is clsely linked with political development and thus by helping them to improve it makes the world a more stable place.
It's all well and good saying leave them to rot, but eventually it will bite you in the ass. Look at the embassy bombings in Kenya and Tanzania, or the 9/11 attacks in the USA.
EDIT: I notice you mention aid...what is that if it is not helping them? We DO need to help them via aid, but aid needs to be well targetted and responsibly dealt out.