We describe magnetization measurements on the heavy rare earth titanate pyrochlores R₂ Ti₂ O₇ , where R = Gd, Dy, Ho, Er, Yb, in the temperature range 1.8-300 K, and the field range 0-70 000 Oe. In these materials magnetism arises from the rare earth ions, while Ti is non-magnetic. Analysis of the low field susceptibility versus temperature curves shows that Gd₂ Ti₂ O₇ has antiferromagnetic coupling ( -9 K), which suggests that it is an example of a frustrated antiferromagnet on the pyrochlore lattice. Er₂ Ti₂ O₇ is likewise found to have a large negative Curie-Weiss temperature, -22 K, which we argue is indicative of antiferromagnetic coupling. Ho₂ Ti₂ O₇ , Dy₂ Ti₂ O₇ and Yb₂ Ti₂ O₇ are found to have weak ferromagnetic coupling ( 2 K, 1 K and 1 K respectively) which may be largely dipolar in origin. Fitting of the high field magnetization versus field curves suggests a strong 1,1,1 single ion anisotropy that identifies these three materials as possible realizations of the ferromagnetic `spin ice' model.