While boron nitride (BN) substrates have been utilized to achieve high electronic mobilities in graphene field effect transistors, it is unclear how other layered two dimensional (2D) crystals influence the electronic performance of graphene. In this Letter, we study the surface morphology of 2D BN, gallium selenide (GaSe), and transition metal dichalcogenides (tungsten disulfide (WS2) and molybdenum disulfide (MoS2)) crystals and their influence on graphene's electronic quality. Atomic force microscopy analysis shows that these crystals have improved surface roughness (root mean square value of only ∼0.1nm) compared to conventional SiO2 substrate. While our results confirm that graphene devices exhibit very high electronic mobility (μ) on BN substrates, graphene devices on WS2 substrates (G/WS2) are equally promising for high quality electronic transport (μ∼ 38000 cm2/V s at room temperature), followed by G/MoS 2 (μ∼ 10000 cm2/V s) and G/GaSe (μ∼ 2200 cm2/V s). However, we observe a significant asymmetry in electron and hole conduction in G/WS2 and G/MoS2 heterostructures, most likely due to the presence of sulphur vacancies in the substrate crystals. GaSe crystals are observed to degrade over time even under ambient conditions, leading to a large hysteresis in graphene transport making it a less suitable substrate. © 2014 AIP Publishing LLC.