1. Apparatus for processing data, said apparatus comprising: one or more registers; and breakpoint circuitry responsive to detection of an access to at least one of said one or more registers to trigger a breakpoint response, wherein said breakpoint circuitry comprises one or more debug registers, said breakpoint circuitry being responsive to register access characterizing data held within respective debug registers to determine characteristics of accesses to a target register of said one or more registers that trigger said breakpoint response, and wherein said register access characterizing data comprises a mask value specifying one or more bits within said target register for which register accesses are monitored by said breakpoint circuitry.