The possibility of using simple sets of planar coils to produce low-aspect-ratio stellarator (LARS) configurations is analysed. Various types of LARS with different planar coils of potential interest to fusion research are identified. It is found that these configurations possess rather attractive features including: compact design and coil simplicity; good access to the plasma; closed vacuum flux surfaces with large enclosed volume; a significant external rotational transform; strong magnetic well; and a natural divertor. Finite plasma-pressure and finite plasma-current effects are studied as well, and it is shown that the LARS configurations considered benefit from the plasma current.