We address the role of the nature of material disorder in determining the roughness of cracks, which grow by damage nucleation and coalescence ahead of the crack tip. We highlight the role of quenched and annealed disorders in relation to the length scales d and xic associated with the disorder and the damage nucleation, respectively. In two related models, one with quenched disorder in which d approximately xic, the other with annealed disorder in which d<<xic, we find qualitatively different roughening properties for the resulting cracks in two dimensions. The first model results in random cracks with an asymptotic roughening exponent zeta approximately 0.5. The second model shows correlated roughening with zeta approximately 0.66. The reasons for the qualitative difference are rationalized and explained.