We present the results of an analysis of time-series photometry, Ca II H and K spectrophotometry, and high-dispersion visible spectra of nine nearby Sun-like stars recently identified as having planets. For the six stars whose presumed planets have orbital periods of less than 4 months (τ Boo, 51 Peg, υ And, ρ1 Cnc, ρ CrB, and 70 Vir), sine-curve fits to the photometric data show no variations with semiamplitude greater than 1 or 2 parts in 104. Photometric variations in 47 UMa are similarly small, although our photometric data of this star are slightly affected by variability of the comparison star. Nonvariability at this level of precision is sufficient to rule out surface magnetic activity as the cause of the observed radial-velocity variations in these seven stars and makes nonradial pulsations unlikely as well. Thus, our photometry provides indirect but strong support for true reflex motions-planets-in these seven stars, but cannot yet so support the planetary hypothesis for the two additional stars, 16 Cyg B and Gl 411. Continued photometric monitoring of the short-period systems may soon result in the direct detection of these planets in reflected light. We have used our photometric fluxes to search for possible transits of the extrasolar planets. Transits definitely do not occur in τ Boo, 51 Peg, υ And, and ρ1 Cnc, and probably do not occur in ρ CrB and 70 Vir. Our transit-search results are inconclusive for 47 UMa, and we cannot address the issue for 16 Cyg B and Gl 411. The precision of our photometry is sufficient to detect transits of planets even if they are not gas giants, as currently assumed, but much smaller objects with rocky compositions. The chance of finding at least one transit in the six stars is ~40%. We find significant year-to-year photometric variability only in τ Boo, which is not only the youngest star in the sample but also the star with the shallowest convective zone. The interseasonal range in its yearly mean photometric flux is ~0.002 mag, roughly twice the 0.0008 mag decadal variation in the Sun's total irradiance. Monitoring of the relative Ca II H and K fluxes began between 1966 and 1968 for 51 Peg, τ Boo, ρ CrB, and Gl 411, between 1990 and 1993 for 47 UMa, 70 Vir, 16 Cyg B, and ρ1 Cnc, and in 1996 for υ And. The data have been newly recalibrated for improved long-term instrumental stability, resulting in better precision of the Ca II records. Five of the nine stars in this study have little or no detectable year-to-year variation in Ca II flux. The remaining four show moderate or pronounced variability: τ Boo, whose radial-velocity and photometric variations have comparatively high amplitudes; Gl 411, whose planetary companion was inferred astrometrically, not spectroscopically; ρ1 Cnc, which may undergo decadal cyclic activity; and υ And, which shows moderate year-to-year variability. Except for 47 UMa, intraseasonal variability consistent with rotation was detected in the Ca II records of all stars. However, the rotation periods determined for υ And, 70 Vir, and 16 Cyg B are of low confidence. An examination of the recalibrated Ca II records for 51 Peg finds a rotation period of 22 days, in contrast to our previous result of 37 days. Ages have been estimated from the mean Ca II flux and, where possible, the rotation period. We find general consistency with the ages determined by others comparing properties determined from high-resolution spectroscopy to evolutionary models, although the uncertainties are, in general, large. Based on observations made at Mount Wilson Observatory, operated by the Mount Wilson Institute, under an agreement with the Carnegie Institution of Washington and the automatic photoelectric telescope at Fairborn Observatory in the Patagonia Mountains of southern Arizona.