In the 78 days of NATO bombing in 1999 known as Operation Allied Force, the best estimates are that 30 tonnes of DU was dropped throughout Serbia (incl Kosovo). In March 2000, NATO admitted to having fired 31,000 DU rounds - mainly from A10 warplanes, but the Yugoslav authorities estimate 50,000 DU rounds.
Unproven suspicions that the US tested new DU-based bunker-buster missiles containing over a tonne of DU each (see Dai Williams report, in this article's section on Weaponisation of DU) may mean the actual amount of DU used was much higher.
The US was the only NATO country to use DU in the Balkans.

In total, NATO flew about 35,000 sorties (a third of them bombing missions), fired 550 cruise missiles and dropped about 23,000 bombs. The proportion of "precision" munitions was 35%, considerably up from Desert Storm, but still not quite the video game portrayed by NATO's PR frontmen.
In July 1999, Ramsey Clark's IAC commenced war crimes hearings against NATO

NATO spokesmen long refused to specify where DU rounds had been fired, before belatedly providing limited maps in March 2000. This was their first official acknowledgement of the use of DU, and the maps identified 28 locations in Kosovo, but none in Serbia proper, even though DU has been reliably discovered there.

After the war, UNEP formed a task force to assess the impacts of the war. However, due to NATO's delay in disclosing DU sites, they were initially reduced to conducting a review of published literature. They finally travelled to Kosovo in November 2000, but only sampled 11 of 112 reported DU target sites, and did not visit Serbia. The sites they sampled had already been visited by NATO troops (and almost certainly cleaned) beforehand. Furthermore, the sites disclosed by NATO were all the targets of A10 raids, and UNEP did not sample any missile or bomb sites. In view of the Dai Williams report suggesting the use of prototype bunker busters with large amounts of DU, this may be a significant omission.
Dr Chris Busby reviewed their report in April 2001 and proclaimed it a whitewash, claiming that the data in their own tables contradicted their conclusions (and significantly, the tables were stripped from the version of the report that was presented to the press conference). He also criticised them for not taking air samples, and concluded there was significant DU contamination in rainwater, and wide dispersion of the ceramic DU aerosol particles. On his own field trip, he measured radiation levels of up to 5,000 Bq/Kg (20 times the safe limit) in dust samples.
Other critics have alleged that UNEP used geiger counters that were incapable of detecting alpha particles, which are the primary radioactive emission of DU.

Articles by the Geneva-based journalist, Robert James Parsons, in the San Francisco Examiner on 1st May 2000 and in The Nation on 9th April 2001 trace the politics of the DU cover-up in Yugoslavia.
The latter article refers to a NATO admission of using 10 tonnes of DU on hardened Serb bunkers, and Robert Fisk had already reported a NATO admission that some cruise missiles contained DU, in The Independent on 22nd November 1999

The so-called "Balkans Syndrome" caused a brief but intense media furore in Europe in late 2000, when NATO peacekeepers began to fall ill. The term was actually coined in advance by Felicity Arbuthnot, in anticipation of what would surely follow any US bombing campaign.
As of January 2001, 6 Italian peacekeepers had died of leukemia (Counterpunch, says 8 by February 2001) after serving in the Balkans, as did 5 Belgians from various cancers, 4 French, 4 Hungarians (although Hungarian TV blamed the Serbs for spreading DU !) 2 Dutch, 2 Spaniards, 1 Portuguese and 1 Czech. Many other cases of cancer have been reported by European troops - see Canadian CBC TV
20% of the 17,000 Belgian troops who served in the Balkans in the 1990s were reporting health problems by September 2000 - Tanjug
On 27th April 2002, the Italian RAI TV station reported 7 deformed births among soldiers who had served in the Balkans.

The highest incidence of leukaemia cases seems to have been for the Mediterranean troops (Italian, Spanish and Portuguese) assigned to western Kosovo, one of the heaviest bombing locations (see Dai Williams report in Weaponisation section, for significance of this - the only DU usage admitted by NATO was the A10's 30mm bullets). US and UK troops were allocated to less heavily bombed regions.

In response, Portugal withdrew its contingent, saying they would not be allowed to become "uranium meat", 400 Norwegian peacekeepers refused to sign service contracts for service in Kosovo, and Greece offered all its peacekeepers the option of withdrawing.
NATO peacekeepers had their food and drink flown in from outside, and Dutch and German soldiers were specifically ordered not to eat local produce. Dutch soldiers stationed around Pritzen sent all their clothing and equipment back to Holland for decontamination, allegedly due to asbestos decontamination, but their vehicles ended up in a radiation decontamination plant.
The UN High Commission for Refugees, the main coordinator of aid to Kosovo, quietly decided to refrain from sending pregnant staff to Kosovo, and to offer staff there the option of reassignment.

America's response to the increasing concern was delivered by Secretary of State, Madeleine Albright. Her advice to Europeans in February 2001 was not to be "excessively nervous and hysterical" about DU (this of course, is the same humanitarian who said a few years earlier, that half a million dead Iraqi children was "worth it").

NATO's Kosovo war only used 5-10% of the DU munitions fired at Iraq in 1991, but the British MoD still saw fit to warn its personnel in Kosovo to stay clear of DU-affected areas, unless wearing full protective clothing. Naturally, no such warning was issued to returning refugees - Felicity Arbuthnot - Sunday Herald, 02 August 1999
Only in 2001, did the US warn Kosovar children not to play on destroyed tanks.

As in the Gulf, western public concern was more focussed on the soldiers who had participated in the DU assault on Yugoslavia, than it was on the real victims - the people of Yugoslavia and the Balkans. Indeed, the UN was careful not to record Yugoslav cancer cases. Also as in the Gulf, the use of DU was just one element in the cocktail of biochemical warfare unleashed by the US, and Yugoslavians quickly dubbed the war an act of ecocide.
See 31 January 2001 article - other reports also speak of the bombing of Pancevo releasing 8 tonnes of mercury into the Danube.
The number of miscarriages in Pancevo doubled in the months after the bombing, and pregnant women were advised to get abortions.

Some researchers reported an 8-fold increase in radioactivity in both Macedonia and Bulgaria, while airborne uranium dust was detected in Greece and Hungary.
In April 2000, Yugoslav officials reported radiation levels of up to 235,000 Bq/kg (1,000 times the safe level) in areas of Serbia proper.
This makes it all the more suspicious that NATO's colleagues in UNEP failed to find any DU contamination in Kosovo.
Reuters - 22 April 2000
Hiroshima daily's special report - describes one of the 235K Bq/kg hot spots

Of course, local civilians are even more subject to the same radiation sources that killed the NATO peacekeepers, but that is less reported.
18 January 2001, Athens News Agency (quoted by Chinese People's Daily) - Serbian scientists report 200% cancer increase in bombed areas of Serbia, and 30% nationwide
Centre for Reasearch on Globalisation - reports January 2001 claim by Yugoslavia's BETA news agency, of a 200% increase in leukemia in Northern Kosovo
BBC, 15 January 2001 - report of cancers and birth deformities in Kosovo
 

Bosnia

It is estimated that 3 tonnes of DU were dropped on Bosnia in 1994-95, when NATO bombed the Bosnian Serbs at the tail-end of the Bosnian war - the grotesquely named Operation Deliberate Force. In December 2000, NATO admitted to having fired 11,000 DU rounds in that campaign.
In total, NATO dropped about 1,000 bombs, and fired 23 cruise missiles.

After the requisite incubation period, the Bosnian Serb Republic now reports a five-fold increase in cancer since the mid-90s bombing campaign, with the same recent exponential increase that had been previously seen in Iraq, eg. cancer cases in the major town of Banja Luka have more than doubled from 1999 to 2000.

The biggest cluster of cancers is amongst the former population of the Sarajevo suburb of Hadzici, which was struck by by several hundred DU projectiles. Now refugees in Bratunac, 10% of this community of almost 4,000 people have died of cancer - CNN, 14 January 2001
There are reports the Bosnian Serb authorities themselves blocked further research on this, under US pressure - Robert Fisk, Independent, 19 January 2001

Dr Chris Busby reports claims of a 10-fold increase in leukemia and lymphoma in Sarajevo - Green Audit, February 2002