Future surveys for transiting extrasolar planets are expected to detect hundreds of jovian-mass planets and tens of terrestrial-mass planets. For many of these newly discovered planets, the intervals between successive transits will be measured with an accuracy of 0.1 to 100 minutes. We show that these timing measurements will allow for the detection of additional planets in the system (not necessarily transiting) by their gravitational interaction with the transiting planet. The transit-time variations depend on the mass of the additional planet, and in some cases terrestrial-mass planets will produce a measurable effect. In systems where two planets are seen to transit, the density of both planets can be determined without radial-velocity observations.