There are institution like Catholic Charity - nasty religious people!!!, they refuse most of things. Then Red Cross - they are the same minus religiosity:-( . There are some special events for collecting old things for homeless people or in case of natural/other disasters, there are official events. Then there are second-hand shops but these are mostly garments. Form time to time, you can find some jumble sales but very rarely. at least here where I live. Prague is a very cosmopolitan city, I am sure there are more opportunities.
I myself loaded a car with thigs after my husband passed away and brought then to my friend who has problems.
Books are a problem, the shops won´t take them apart from some exclusive intems...