According to Human Rights Watch, an international NGO (non-governmental organization) dedicated toward the preservation and monitoring of human rights and human rights abuses (respectively), during the air war by US and "coalition forces" (Mar. 19 through Apr. 09, specifically), over 29,000 (29,199, to be precise) bombs were dropped on Iraq, out of which 31% were not "precision-guided" warheads. The heavily concentrated bombing campaign on Baghdad and other major cities in Iraq earlier this year has led to the deaths of approximately 3,000 Iraqi civilians, according to HRW and Associated Press estimates. However, according to this, the count much higher.

You can read the report ("Off Target: The Conduct of the War and Civilian Casualties in Iraq") here. There is a downloadable version of the publication in PDF format (16 MB).