We are often offered donations. We only accept them on the proviso that we can offer them to other libraries, sell them or pass them on to students. The items passed onto student are usually old copies of magazines. If the donor rings first I will try to ascertain just what they have on offer and may recommend somewhere else for them to offer them to.
However sometimes the donations turn up in the library without a phone call first.
My experiecne is that most donors are OK with items being passed on or sold.

Hi Christine

As a small library with a tiny budget, we do accept donations, but do so on the proviso that the donor is happy for us to pass them on to other libraries or to sell them to raise funds where appropriate. We have a storeroom where we are holding books that we plan to sell to students in a fundraiser and this will be the only cost recovery available to us.

We almost always have a backlog of donations to process, but we do find that we receive a lot of valuable books that we do actually need, so it is worth the effort. We are careful, though, to find out exactly what is being offered before accepting. We have turned away some donations that are clearly no use to us, other libraries, or even as sale items.

Kelly - National Art School