Scanning tunneling spectroscopy is used to investigate the single-electron states and the corresponding squared wave functions of single and freestanding strain-induced InAs quantum dots grown on GaAs(001). Several peaks are found in dI/dV curves, which belong to different single-electron states. Spatially resolved dI/dV images reveal (000), (100), (010), (200), and (300) states, where the numbers describe the number of nodes in {[}1 (1) over bar0], {[}110], and {[}001] directions, respectively. The total number and energetic sequence of states is different for different dots. Interestingly, the (010) state is often missing, even when (200) and (300) states are present. We interpret this anisotropy in electronic structure as a consequence of the shape asymmetry of the dots.