We experimentally demonstrate novel structures for the realization of registers of atomic qubits: We trap neutral atoms in one- and two-dimensional arrays of far-detuned dipole traps obtained by focusing a red-detuned laser beam with a microfabricated array of microlenses. We are able to selectively address individual trap sites due to their large lateral separation of 125   μm. We initialize and read out different internal states for the individual sites. We also create two interleaved sets of trap arrays with adjustable separation, as required for many proposed implementations of quantum gate operations.