Long-duration gamma-ray bursts (GRBs) are widely believed to be highly collimated explosions (bipolar conical outflows with half-opening angle theta{approx} 1{sup 0}-10{sup 0}). As a result of this beaming factor, the true energy release from a GRB is usually several orders of magnitude smaller than the observed isotropic value. Measuring this opening angle, typically inferred from an achromatic steepening in the afterglow light curve (a 'jet' break), has proven exceedingly difficult in the Swift era. Here, we undertake a study of five of the brightest (in terms of the isotropic prompt gamma-ray energy release, E{sub g}amma{sub ,iso}) GRBs in the Swift era to search for jet breaks and hence constrain the collimation-corrected energy release. We present multi-wavelength (radio through X-ray) observations of GRBs 050820A, 060418, and 080319B, and construct afterglow models to extract the opening angle and beaming-corrected energy release for all three events. Together with results from previous analyses of GRBs 050904 and 070125, we find evidence for an achromatic jet break in all five events, strongly supporting the canonical picture of GRBs as collimated explosions. The most natural explanation for the lack of observed jet breaks from most Swift GRBs is therefore selection effects. However, the opening angles for the events in our sample are larger than would be expected if all GRBs had a canonical energy release of {approx}10{sup 51} erg. The total energy release we measure for the 'hyper-energetic' (E{sub tot} {approx}> 10{sup 52} erg) events in our sample is large enough to start challenging models with a magnetar as the compact central remnant.