U238 itself is primarily a low-level alpha emitter, but its decay products such as Thorium (Th-234) and Proactinium (Pa-234) are energetic Beta emitters, and within a year of creating a new batch of DU, these progeny exist in considerable quantities. Further down the decay chain, come the radon daughters, emitting significant alpha and beta radiation.
See WISE, for uranium's decay chain.

When a DU projectile hits a target, up to 70% of the DU burns, bursting into highly toxic, radioactive microscopic uranium oxide particles - effectively creating a ceramic DU aerosol. Most of the particles are of respirable size (less than 10 microns), ie. they're small enough to be ingested via inhalation (and certainly via open wounds), and can be carried long distances (25 miles or more) by the wind, before settling. They can then be resuspended again by wind or movement, and dispersed yet further. They can also migrate long distances via the ground water table. Once deposited in the lungs, kidneys or bone, DU particles generally remain in the body for many years.
This ceramic formation is important, because it is highly insoluble in lung fluids, unlike the traditional uranium dust encountered by miners, which is rapidly excreted. Indeed, Gulf War vets are still passing DU in their urine 12 years on.
The unoxidised DU fragments left in the open eventually rust away into a very fine black dust, and spread through the air and water. The DU fragments, oxides and dust obviously have the same radiological properties, but differ in their concentration, and in their patterns of absorption into the environment and living beings.

DU's alpha and beta particle radiation have limited ranges of penetration and hence are not expected to cause serious damage to living tissue via external exposure. However, it is the internal exposure to tissue that makes ingested DU particles such a hazardous radioactive source, and its alpha particles cause significant internal ionisation, resulting in cell death and genetic mutations in exposed individuals, and genetic abnormalities in their descendents over the generations.
See Dr Bertell, (IICPH, August 1999) for a discussion of the ceramic particles, and their longevity in the body. In fact, Dr Bertell describes DU as a "very powerful alpha emitter".

In the IAC's 1997 book Metal of Dishonor: Depleted Uranium, co-author John Catalinotto claims that the radioactive dosage from a single ingested particle of DU, is equivalent to one chest X-ray per hour, for life (or what remains of it).

US forces (probably Doug Rokke's men) have measured DU fragments in the Gulf emitting up to 250 millirads of radiation per hour, and the US military are on record as confirming 2.5mGy/hr at the surface of a DU shell.
Each A-10 (American warplane) 30mm cannon anti tank shell contains some 275g of DU (10.1 Bq of activity).

Retired nuclear scientist, Leonard Dietz (currently working for the UMRC), has estimated the radiation dose from a 5-micrometer (ie. small enough to inhale) DU oxide particle in the lung, as being 1360 rem per year. This is 272 times the maximum permissible dose for radiation workers and 800 times the permitted dose for the general population.

Additionally, the evidence of contamination with enriched uranium and plutonium (see Cover Up section) means that DU may be vastly more radioactive than we would expect due to U238 alone.

As we all know, the hazards of radiation include cancers and genetic mutations, and U238's radiological effects last for 4.5 billion years (could this be what Bush meant, when he spoke of waging war without end ?).
These photos on TFTT show some resulting extreme birth deformities in Iraq (and amongst US vets).
Not surprisingly, many commentators have compared the use of DU weapons to low-level nuclear warfare.

As a heavy metal (in fact the heaviest), DU also exhibits high levels of chemical toxicity, with all the associated health hazards, including kidney damage, arterial damage, and cancer.
Health guidelines on the max acceptable concentrations of various toxic substances reveal DU to be on a par with lead arsenate, and more dangerous than phosgene or arsenic. Some experts believe DU's chemical toxicity outweighs the radiological damage - Le Monde, February 2001

 
See TFTT's Scientific Argument Against DU, for more info on the dangers.
Note especially the October 1999 article by Prof Margaret Ryle, demonstrating that due to its complex decay chain, and the localised nature of the radiation from the immobilised ceramic particles, U238 may in fact be much more radiologically dangerous, than its relatively low radioactivity would suggest.
The phenomenon resulting from U238's particular decay chain (ie. its characteristic sequence of radioactive emissions) is known as as Busby's Second Event theory, and is further documented on the LLRC website, and in Dr Chris Busby's 1995 book, Wings of Death. This theory basically states that the probability of cellular DNA damage (ie. mutation) is magnified many times, for isotopes like U238.
As for the significance of the term "localised" radiation, that refers to the fact that the nuclear industry's standard model for estimating radioactive exposure (as propounded by the ICRP) is based on average whole-body exposure from an external source, and does not take into account the magnified localised effects of concentrated irradiation by an immobilised internal source of radiation (eg. a DU particle lodged in the lungs or bone marrow). The LLRC therefore believe that applying the ICRP's radiology model to DU is fatally flawed, because over a prolonged period of time, although such a DU particle will emit a radiation dose which may appear mild if averaged over the whole body, since this dose is actually concentrated in the surrounding tissue, it has a severe effect on that part of the body. In fact, the LLRC website states:
A single particle of DU smaller than 5 microns can expose the surrounding tissue to radiation 800 times the annual dosage permitted by the Nuclear Regulatory Commission (NRC) for the entire body.