There are re-cycling points all around town for the common re-cyclables such as glass, paper and cans. They also re-cycle fridges. In the city there's a door to door paper collection scheme.
For the rest the Butt Lane dump and re-cycling centre between Milton and Histon just north of the A14 has facilities to re-cycle: cardboard, paper, and other compostable waste, glass, oil, metal, hard core, soil, batteries, clothing, household goods and fridges. Opening hours: Apr-Sep: Mon-Fri 9:00-20:00, Sat-Sun 09:00-18:00; Oct-Mar: 09:00-dusk.
A comprehensive re-cycling directory is available free from Mandela house on Regent Street, Friends of the Earth at the Bath House on Gwydir St, or local libraries.
There appear to be no facilities in the City for re-cycling wood; however there are enough people with open fires lurking in cam.misc that someone will probably take it off your hands.