We apply machine learning in the form of a nearest neighbor instance-based algorithm (NN) to generate full photometric redshift probability density functions (PDFs) for objects in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS DR5). We use a conceptually simple but novel application of NN to generate the PDFs - perturbing the object colors by their measurement error - and using the resulting instances of nearest neighbor distributions to generate numerous individual redshifts. When the redshifts are compared to existing SDSS spectroscopic data, we find that the mean value of each PDF has a dispersion between the photometric and spectroscopic redshift consistent with other machine learning techniques, being sigma = 0.0207 +/- 0.0001 for main sample galaxies to r < 17.77 mag, sigma = 0.0243 +/- 0.0002 for luminous red galaxies to r < ~19.2 mag, and sigma = 0.343 +/- 0.005 for quasars to i < 20.3 mag. The PDFs allow the selection of subsets with improved statistics. For quasars, the improvement is dramatic: for those with a single peak in their probability distribution, the dispersion is reduced from 0.343 to sigma = 0.117 +/- 0.010, and the photometric redshift is within 0.3 of the spectroscopic redshift for 99.3 +/- 0.1% of the objects. Thus, for this optical quasar sample, we can virtually eliminate catastrophic photometric redshift estimates. In addition to the SDSS sample, we incorporate ultraviolet photometry from the Third Data Release of the Galaxy Evolution Explorer All-Sky Imaging Survey (GALEX AIS GR3) to create PDFs for objects seen in both surveys. For quasars, the increased coverage of the observed frame UV of the SED results in significant improvement over the full SDSS sample, with sigma = 0.234 +/- 0.010. We demonstrate that this improvement is genuine. [Abridged]
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