Actual book-borers are uncommon. Both the larvae of the death watch beetle (Xestobium rufovillosum) and the common furniture beetle (Anobium punctatum) will tunnel through wood and if paper is nearby they will pass into that.
A major book-feeding insect is the booklouse (or book louse). A tiny (under 1 mm), soft-bodied wingless psocoptera (usually Trogium pulsatorium), that actually feeds on molds and other organic matter found in ill-maintained works, although they will also attack bindings and other parts. It is not actually a true louse.
Many other insects, like the silverfish (Lepisma saccharina) or cockroach (various Blattodea), will consume these molds and also degraded paper or the starch-based binding pastes – warmth and moisture or high humidity are prerequisites, so damage is more common in the tropics. Modern glues and paper are less attractive to insects.
Tineola bisselliella and Hofmannophila pseudospretella will attack cloth bindings. Leather bound books attract various consumers, such as Dermestes lardarius and the larvae of Attagenus unicolor and Stegobium paniceum.