We discuss the phenomenon of laser-induced level crossings in molecular systems, and we show how such crossings may be created and explored. The problem is formulated in terms of Born-Oppenheimer states coupled by electric dipole transitions. We specify the problem to a pair of crossing levels, and integrate the coupled motion of wave packets on these levels. The results of the calculation are compared with the Landau-Zener approximation; agreement is found for most parameter ranges, when the classically calculated velocity at the crossing is introduced into the Landau-Zener adiabaticity parameter. For cases when no actual crossing is encountered we observe features characteristic of the wave mechanical nature of the situation, namely: tunneling, split up of the packets and interference.