Researchers are increasingly acknowledging the important role of complex networks in numerous scientific contexts. In this paper we define two kinds of motifs - bridge and brick - for exploring and predicting network behaviors and functions and for identifying differences among network structures. Based on an analysis of these motifs in genetic, social, ecological, and engineering networks, we found significant differences in motif functionality and topology. After initially observing similarities between social networks and their genetic, ecological, and engineering counterparts, we eventually noted greater amounts of brick motif in social networks and greater amounts of bridge motif in the other three types. Our conclusion is that bridge and brick motif content analyses can assist researchers in understanding the small-world and clustering properties of network structures and in investigating network functions and behaviors.