Results from ab initio electronic structure theory calculations on model systems allow for the detailed comparison of tunneling through covalently bonded contacts, hydrogen bonds, and van der Waals contacts. Considerable geometrical sensitivity as well as an exponential distance dependence of the tunneling is observed for tunneling through various nonbonded contacts. However, the fundamental result from the present study is that at most a modest difference is observed between tunneling mediated by H-bonds and tunneling mediated by van der Waals contacts at typical distances for each type of interaction. These results are considered in relation to the pathways model of Beratan and Onuchic, and implications for understanding long-range tunneling in biological systems are discussed.