The strong spontaneous polarization and piezoelectric effects in the wurtzite IIInitride semiconductors lead to new possibilities for device design. In typical heterojunction field effect transistors these effects are used to create large electron concentrations at the AlGaN/GaN interface. However, we examine several other possible device structures which include heterojunctions of AlGaN, GaN, and InGaN. For example, we find the strong electric fields present in these structures allow us to create quantum wells greater than 1 eV deep. Both Ga-faced and N-faced materials are explored. The two-dimensional electron gas concentrations in these structures are found using a self-consistent 1-D Schrödinger-Poisson solver modified to incorporate the effects of spontaneous and piezoelectric polarization. The boundary conditions at the heterojunction interfaces and at the surface and substrate are discussed in detail. Electron concentrations are compared with those obtained experimentally through capacitance-voltage and Hall effect measurements.