This work studies the achievable secure rate per source-destination pair in wireless networks. First, a path loss model is considered, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes with intensities $λ$ and $λ_e$, respectively. It is shown that, as long as $λ_e/λ=o((\log n)^{-2})$, almost all of the nodes achieve a perfectly secure rate of $Ω(\frac{1}{\sqrt{n}})$ for the extended and dense network models. Therefore, under these assumptions, securing the network does not entail a loss in the per-node throughput. The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Secondly, an ergodic fading model with $n$ source-destination pairs and $n_e$ eavesdroppers is considered. Employing the ergodic interference alignment scheme with an appropriate secrecy pre-coding, each user is shown to achieve a constant positive secret rate for sufficiently large $n$. Remarkably, the scheme does not require eavesdropper CSI (only the statistical knowledge is assumed) and the secure throughput per node increases as we add more legitimate users to the network in this setting. Finally, the effect of eavesdropper collusion on the performance of the proposed schemes is characterized.