Many existing and proposed experiments targeting QCD axion dark matter (DM) can also search for a broad class of axionlike particles (ALPs). We analyze the experimental sensitivities to electromagnetically coupled ALP DM in different cosmological scenarios with the relic abundance set by the misalignment mechanism. We obtain benchmark DM targets for the standard thermal cosmology, a pre-nucleosynthesis period of early matter domination, and a period of kination. These targets are theoretically simple and assume Oð1Þ misalignment angles, avoiding fine-tuning of the initial conditions. We find that some experiments will have sensitivity to these ALP DM targets before they are sensitive to the QCD axion, and others can potentially reach interesting targets below the QCD band. The ALP DM abundance also depends on the origin of the ALP mass. Temperature-dependent masses that are generated by strong dynamics (as for the QCD axion) correspond to DM candidates with smaller decay constants, resulting in even better detection prospects.