The reactions between Al+(3(1)S) and O-3, O-2, N-2, CO2 and H2O were studied using the pulsed laser ablation at 532 nm of an aluminium metal target in a fast flow tube, with mass spectrometric detection of Al+ and AlO+. The rate coefficient for the reaction of Al+ with O-3 is k(293 K) = (1.4 +/- 0.1) x 10(-9) cm(3) molecule(-1) s(-1); the reaction proceeds at the ion-dipole enhanced Langevin capture frequency with a predicted T-0.16 dependence. For the recombination reactions, electronic structure theory calculations were combined with Rice-Ramsperger-Kassel-Markus theory to extrapolate the measured rate coefficients to the temperature and pressure conditions of planetary ionospheres. The following low-pressure limiting rate coefficients were obtained for T = 120-400 K and He bath gas (in cm(6) molecule(-2) s(-1), uncertainty +/-sigma at 180 K): log(10)(k, Al+ + N-2) = -27.9739 + 0.05036 log(10)(T) - 0.60987(log(10)(T))(2), sigma = 12%; log(10)(k, Al+ + CO2) = -33.6387 + 7.0522 log(10)(T) - 2.1467(log(10)(T))(2), sigma =13%; log(10)(k, Al+ + H2O) = -24.7835 + 0.018833 log(10)(T) - 0.6436(log(10)(T))(2), sigma = 27%. The Al+ + O-2 reaction was not observed, consistent with a D degrees(Al+-O-2) bond strength of only 12 kJ mol(-1). Two reactions of AlO+ were also studied: k(AlO+ + O-3, 293 K) = (1.3 +/- 0.6) x 10(-9) cm(3) molecule(-1) s(-1), with (63 +/- 9)% forming Al+ as opposed to OAlO+; and k(AlO+ + H2O, 293 K) = (9 +/- 4) x 10(-10) cm(3) molecule(-1) s(-1). The chemistry of Al+ in the ionospheres of Earth and Mars is then discussed.