In this paper, we present and investigate a model for solid tumor growth that incorporates features of the tumor microenvironment. Using analysis and nonlinear numerical simulations, we explore the effects of the interaction between the genetic characteristics of the tumor and the tumor microenvironment on the resulting tumor progression and morphology. We find that the range of morphological responses can be placed in three categories that depend primarily upon the tumor microenvironment: tissue invasion via fragmentation due to a hypoxic microenvironment; fingering, invasive growth into nutrient rich, biomechanically unresponsive tissue; and compact growth into nutrient rich, biomechanically responsive tissue. We found that the qualitative behavior of the tumor morphologies was similar across a broad range of parameters that govern the tumor genetic characteristics. Our findings demonstrate the importance of the impact of microenvironment on tumor growth and morphology and have important implications for cancer therapy. In particular, if a treatment impairs nutrient transport in the external tissue (e.g., by anti-angiogenic therapy) increased tumor fragmentation may result, and therapy-induced changes to the biomechanical properties of the tumor or the microenvironment (e.g., anti-invasion therapy) may push the tumor in or out of the invasive fingering regime.