We present a search for Trojan companions to 25 transiting exoplanets. We use the technique of Ford & Gaudi, in which a difference is sought between the observed transit time and the transit time that is calculated by fitting a two-body Keplerian orbit to the radial-velocity data. This technique is sensitive to the imbalance of mass at the L4/L5 points of the planet-star orbit. No companions were detected above 2σ confidence. The median 2σ upper limit is 56 M _⊕, and the most constraining limit is 2.8 M _⊕ for the case of GJ 436. A similar survey using forthcoming data from the Kepler satellite mission, along with the radial-velocity data that will be needed to confirm transit candidates, will be sensitive to 10-50 M _⊕ Trojan companions in the habitable zones of their parent stars. As a by-product of this study, we present empirical constraints on the eccentricities of the planetary orbits, including those which have previously been assumed to be circular. The limits on eccentricity are of interest for investigations of tidal circularization and for bounding possible systematic errors in the measured planetary radii and the predicted times of secondary eclipses.