We present initial results from our ongoing program to image the Sunyaev-Zel'dovich (SZ) effect in galaxy clusters at 143 GHz using Bolocam; five clusters and one blank field are described in this manuscript. The images have a resolution of 58 arcsec and a radius of 6-7 arcmin, which is approximately r 500-2r 500 for these clusters. We effectively high-pass filter our data in order to subtract noise sourced by atmospheric fluctuations, but we are able to obtain unbiased images of the clusters by deconvolving the effects of this filter. The beam-smoothed rms is 10 Delta *mKCMB in these images; with this sensitivity, we are able to detect the SZ signal to beyond r 500 in binned radial profiles. We have fit our images to beta and Nagai models, fixing spherical symmetry or allowing for ellipticity in the plane of the sky, and we find that the best-fit parameter values are in general consistent with those obtained from other X-ray and SZ data. Our data show no clear preference for the Nagai model or the beta model due to the limited spatial dynamic range of our images. However, our data show a definitive preference for elliptical models over spherical models, quantified by an F ratio of 20 for the two models. The weighted mean ellipticity of the five clusters is = 0.27 ? 0.03, consistent with results from X-ray data. Additionally, we obtain model-independent estimates of Y 500, the integrated SZ y-parameter over the cluster face to a radius of r 500, with systematics-dominated uncertainties of 10%. Our Y 500 values, which are free from the biases associated with model-derived Y 500 values, scale with cluster mass in a way that is consistent with both self-similar predictions and expectations of a 10% intrinsic scatter.