We probe the structure and composition of the atmospheres of five hot Jupiter exoplanets using the Hubble Space Telescope Wide Field Camera 3 (WFC3) instrument. We use the G141 grism (1.1-1.7 μm) to study TrES-2b, TrES-4b, and CoRoT-1b in transit; TrES-3b in secondary eclipse; and WASP-4b in both. This wavelength region includes a predicted absorption feature from water at 1.4 μm, which we expect to be nondegenerate with the other molecules that are likely to be abundant for hydrocarbon-poor (e.g., solar composition) hot Jupiter atmospheres. We divide our wavelength regions into 10 bins. For each bin we produce a spectrophotometric light curve spanning the time of transit or eclipse. We correct these light curves for instrumental systematics without reference to an instrument model. For our transmission spectra, our mean 1σ precision per bin corresponds to variations of 2.1, 2.8, and 3.0 atmospheric scale heights for TrES-2b, TrES-4b, and CoRoT-1b, respectively. We find featureless spectra for these three planets. We are unable to extract a robust transmission spectrum for WASP-4b. For our dayside emission spectra, our mean 1σ precision per bin corresponds to a planet-to-star flux ratio of 1.5 × 10–4 and 2.1 × 10–4 for WASP-4b and TrES-3b, respectively. We combine these estimates with previous broadband measurements and conclude that for both planets isothermal atmospheres are disfavored. We find no signs of features due to water. We confirm that WFC3 is suitable for studies of transiting exoplanets, but in staring mode multivisit campaigns are necessary to place strong constraints on water abundance.