We present new evidence that the amplitude of the two-point correlation function of rich clusters of galaxies has been overestimated due to difficulties in selecting uniform samples of clusters. We have analysed spatial correlations in two redshift samples, Shectman's survey of Lick clusters and a new deep survey of Abell clusters. In each case we find clear evidence that the clustering pattern is strongly anisotropic in redshift space and hence that the catalogues are biased by projection effects. The redshift-space anisotropies are similar to those found for nearby Abell clusters. We show that the scaling test of the angular correlation function for distant Abell clusters is of limited accuracy. Furthermore, our analysis of the deep redshift survey of Huchra et al provides strong evidence that most of the angular clustering for D >= 5 Abell clusters is spurious. Plate-to-plate variations are also shown to produce some artificial angular clustering. Our results suggest a correlation length for Abell clusters r_0_ ~14 h^-1^ Mpc with large uncertainties; thus the existing cluster data cannot provide strong constraints on theoretical models.