I declare myself just as a Muslim. I think Muslims everywhere, regardless of whatgroup they may perceive themselves to belong to, have not much cared about the 'differences.' If I meet a Muslim I never ask him/her if they are Shi'a, Sunni, Ahmadi, etc. I simply do not care about that because I do not believe that there need to be divisions. There is only One God, One Islaam.
Why is there fighting? Corrupt leaders, social injustices that have been very slowly worked on (Muslim women's rights, respect for other religious minorities, etc), divisions/rise in sects, etc.
One Hadith, I think, states that Prophet Muhammad savs prophesized a genocide against his descendants. I think this prophecy either fullfilled itself or at least partially it did with the murders of Ali ra and his two sons. Even then the civil war that broke, I believe it happened because of the infiltration of the enemies of our faith and the enemies of the Prophet savs. Holy Qur'an mentions hypocrites during the Prophet's savs time and we can surly say that they did not cease to exist after his death. Perhaps the hypocrites just got stronger, knowing well that the Prophet's savs leadership meant a lot to the Muslim Community's strenght. He held us all together.
Also, I think that there is a big media propaganda going on. It is portrayed that the foreigners are the 'saviors' of Shi'a Muslims of Iraq and that majority of Sunni Iraqis are pro-Sadaam, etc. I feel that the Iraqi Sunnis are rather bitter that the strangers are ruling in their land, and they are told the Shi'a let them in. By the time both Shi'a and Sunni realize that they are both played like a violin, it may cost them a million of lives.