I guess the risk increases as the amount in the body increases. Quite clearly if people have bit of depleted uranium metal in them—which some of the people involved in the friendly fire incidents both on the U.S. and U.K. sides do have—they will have the highest amounts of uranium in their bodies and would be at highest risk. But the studies done in the U.S. have not shown any adverse effects in these people, to the point that they've not considered it necessary to remove all of the shrapnel. They've removed the big bits but often they've left smaller pieces of shrapnel in the individuals concerned. There's no evidence of any toxicity.
Many other metals are much more toxic, including the conventional rounds that are used by the armour-piercing rounds, which contain nickel and cobalt and tungsten. If you look at it from a chemical toxicity point of view, they're probably much more toxic than depleted uranium. Uranium is not very toxic as a material. I would quite happily wear a watch made of depleted uranium, except that it tends to oxidize and my arm and my shirt would be black. Other than that, it wouldn't worry me because the radiation under that piece of uranium would never reach a level where I would expect to see any damage to my skin.
Similarly, if I completely surrounded myself with gamma rays from depleted uranium, I wouldn't exceed the radiation worth a dose limit in a year. If I wanted to get up to the same dose that I get every year from natural background radiation, I'd have to eat about a teaspoonful of uranium, about five grams.