We have measured rotational velocities and oxygen abundances in 29 blue horizontal-branch (BHB) stars in M13, 22 in M3, and 16 in NGC 288 from high-resolution spectra of the O I triplet at 7771-7775 Angstrom. Here we outline the behavior of rotation and oxygen line strength with stellar effective temperature T-eff within each cluster and compare the average values of each from cluster to cluster. The mean strength of the oxygen lines is greatest in NGC 288 and weakest in M3. Within each cluster, the oxygen abundances are nearly constant among stars of a given T-eff but may decrease with increasing T-eff. Among the BHB stars cooler than 10,000 K, there is no sign of the counterparts to the super-oxygen-poor giants which dominate the bright end of the giant branch in M13. The stars hotter than T-eff = 11,500 K show no oxygen lines at all. While these faint blue stars have poorly exposed spectra and may be hot enough to ionize oxygen, the abruptness of the disappearance of the O I lines suggests that either the oxygen abundances are truly low or diffusion sets in abruptly at this color. No star in any cluster rotates more rapidly than 40 km s(-1). Thus [upsilon sin i] is much lower in BHBs than in the superficially similar Population I B8 V-A7 V main-sequence stars. In M13, there is no obvious dependence of upsilon sin i on horizontal-branch (HE) color. The distribution of upsilon sin i values in that cluster can be matched only with a bimodal or otherwise non-Gaussian distribution of upsilon values. Rotational velocities are largest in M13, where six stars have v sin i greater than or equal to 30 km s(-1), and are much smaller in M3 and NGC 288, with none at this level. Since both M13 and NGC 288 have very blue HBs, this indicates that rotation and oxygen abundance are not enough by themselves to determine HE color, either alone or together; another factor such as age must also be at work. Thus, the ''second-parameter'' problem involves more than one such parameter, whose relative influence varies among clusters.