We study the behaviour of packet delays and inter-forwarding times in vehicular networks utilizing opportunistic communication protocols. Our results are obtained through an extensive simulation campaign employing realistic models of vehicular mobility and scenarios derived from real urban environments. We also explore the impact of different forwarding strategies and traffic types on the results. Fitting of probability distributions is carried out for all results, clearly demonstrating the heavy-tailed behaviour of packet delays, inter-forwarding times as well as inter-contact times. In particular, exponential distribution occasionally assumed in analytical studies is strongly ruled out even as a viable approximation for inter-contact times.