We have analyzed nearly all images of the Taurus star-forming region at 3.6-24um that were obtained during the cryogenic mission of the Spitzer Space Telescope (46 deg^2) and have measured photometry for all known members of the region that are within these data, corresponding to 348 sources. We have classified the members of Taurus according to whether they show evidence of disks and envelopes (classes I, II, and III). The disk fraction in Taurus is 75% for solar-mass stars and declines to 45% for low-mass stars and brown dwarfs (0.01-0.3 M_sun). This dependence on stellar mass is similar to that measured for Cha I, although the disk fraction in Taurus is slightly higher overall, probably because of its younger age (1 vs. 2-3 Myr). In comparison, the disk fraction for solar-mass stars is much lower (20%) in IC 348 and Sigma Ori, which are denser than Taurus and Cha I and are roughly coeval with the latter. These data indicate that disk lifetimes for solar-mass stars are longer in regions that have lower stellar densities. Through an analysis of multiple epochs of photometry that are available for ~200 Taurus members, we find that stars with disks exhibit significantly greater mid-IR variability than diskless stars. Finally, we have used our data in Taurus to refine the criteria for primordial, evolved, and transitional disks. The number ratio of evolved and transitional disks to primordial disks in Taurus is 15/98 for K5-M5, indicating a timescale of 0.15 x tau(primordial)=0.45 Myr for the clearing of the inner regions of optically thick disks. After applying the same criteria to older clusters (2-10 Myr), we find that the proportions of evolved and transitional disks in those populations are consistent with the measurements in Taurus when their star formation histories are properly taken into account. ERRATUM: In Table 7, we inadvertently omitted the spectral type bins in which class II sources were placed in Table 8 based on their bolometric luminosities (applies only to stars that lack spectroscopic classifications). The bins were K6-M3.5 for FT Tau, DK Tau B, and IRAS 04370+2559, M3.5-M6 for IRAS 04200+2759, IT Tau B, and ITG 1, and M6-M8 for IRAS 04325+2402 C. In addition, the values of K_s-[3.6] in Table 13 and Figure 26 for spectral types of M4-M9 are incorrect. We present corrected versions of Table 13 and Figure 26.
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