I was told that most aircraft had depleted uranium on board as counterweights. I have not seen one myself. Do all current modern aircraft have depleted uranium on board?
From my research, it looks like about 0.1% of all aircraft carry depleted uranium counterweights.
The Systematic Radiological Assessment of Exemptions for Source and Byproduct Materials (NUREG-1717), on page 3–260, gives a table showing that 430 domestic United States aircraft were delivered with depleted uranium counterweights, and says that "A reasonable estimate is that 50% of these aircraft still contain DU counterweights." So there are about 200 aircraft in the United States which contain depleted uranium counterweights.
Meanwhile, the FAA's "Air Traffic by the Numbers" publication says that there are over 200,000 aircraft in the United States currently.
So no, very few aircraft use depleted uranium counterweights.
That material is dangerous and expensive. It is used only in special situations where the design requirements are stringent and heavily constrained.
For example, the C-5A cargo plane used depleted uranium (DU) to counterweight its main control surfaces.