Gamdwelf, most soldiers are not exposed to DU shells in any way whatsoever. See below.
I'd also like to highlight for most people that DU tends to be used almost solely in Anti-armour weaponry - tank shells, 30mm cannon shells, etc, not small arms ammunition (Rifles, machine guns, etc), and tank armour - the M1A3 has some DU in there to keep it tough. I believe the T90 does the same, not that there are any in Iraq or Afghanistan to my knowledge.
While I don't dispute the logic and possibility that depleted uranium, when it starts to break down definitely could cause problems, I wouldn't figure it's common enough to blame for all the increases in cancer cases as quoted by one person above - I'd say more likely there is a breakdown in infrastructure and higher prevalence of common carcinogens such as degrading plastic and fumes from fires. Ingestion or inhalation of DU is far more likely to cause stomach or lung cancer than Leukaemia.
Furthermore, can someone cite sources for all the problems DU is causing?