While benzene, a typical molecule with ring currents, fails to to fulfill all three requirements, we successfully propose both cyclic and linear molecules as candidates where all three requirements are fulfilled. In annulenes it is essential to consider the bond-length alternation pattern to achieve unidirectional ring currents. As a top candidate we show that the magnetic field in a functionalized dehydro [12]annulene almost reaches a mT. We explore the ring currents in functionalized cumulenes, which are linear carbon molecules, and find that the magnetic field can reach the tesla-range due to the small diameter of the ring currents that appear around the carbon chain.