Some exercises to do at a desk include v-sits and performing a posture check, as stated by Prevention magazine. To do a v-sit, sit on the edge of the chair, lean back and contract the abs to lift each knee up individually. Sitting with good posture forces the core to engage the abdominal muscles in order to keep the back flat and shoulders back.
A simple way to incorporate ab exercise while sitting at a desk is to replace a standard desk chair with an inflatable exercise ball, as stated by WebMD. Just sitting on the exercise ball forces the sitter to work the abdominal muscles so that he remains stable. In a pinch, the sitter can lie back on the ball and perform regular or reverse crunches.