Emerging non-volatile memory (NVM) technologies, such as spin-transfer torque RAM (STT-RAM), are attractive options for replacing or augmenting SRAM in implementing last-level caches (LLCs). However, the asymmetric read/write energy and latency associated with NVM introduces new challenges in designing caches where, in contrast to SRAM, dynamic energy from write operations can be responsible for a larger fraction of total cache energy than leakage. These properties lead to the fact that no single traditional inclusion policy being dominant in terms of LLC energy consumption for asymmetric LLCs. We propose a novel selective inclusion policy, Loop-block-Aware Policy (LAP), to reduce energy consumption in LLCs with asymmetric read/write properties. In order to eliminate redundant writes to the LLC, LAP incorporates advantages from both non-inclusive and exclusive designs to selectively cache only part of upper-level data in the LLC. Results show that LAP outperforms other variants of selective inclusion policies and consumes 20% and 12% less energy than non-inclusive and exclusive STT-RAM-based LLCs, respectively. We extend LAP to a system with SRAM/STT-RAM hybrid LLCs to achieve energy-efficient data placement, reducing the energy consumption by 22% and 15% over non-inclusion and exclusion on average, with average-case performance improvements, small worst-case performance loss, and minimal hardware overheads.