I see this sometimes in Ireland too (on the rare occasion I actually meet people when out and about). Portal tombs generally fall victim to this as they are easy to climb on. Browne's Hill dolmen in Carlow always has tourists climbing all over it and generally about 3 coke cans and few crisp packets in the chamber. Worth than that is when people "worship" at the sites and leave candle wax and things all over the stones...however, that's generally rare in Ireland I find.

Ironically, although I urge people to never climb or interfere with the stones I found a picture of a teenage me stood on the skeletal remains of a passage tomb...I hang my head in shame haha...