The paper gives examples of knots with equal knot polynomials, but distinct signatures, 4-genera, double branched cover homology groups and unknotting numbers. This generalizes some examples given by Lickorish and Millett. It is also shown that there are knots with minimal (crossing number) diagrams of different unknotting number (thus answering a question of Bleiler), and an alternative proof is given of Rudolph's result that there are knots of [les ] 15n crossings with unit Alexander polynomial and 4-genus or unknotting number n.