To play old platform games (as in old platforms, not just old games) on a PC, you need an emulator. Among the best is Mednafen, a multiplatform emulation frontend that brings some favorite platforms--such as NES, every incarnation of GameBoy, and PC-Engine (a.k.a. Turbografx) under one roof. Bust most users will want to download a GUI to avoid pulling their hair out trying to make the emulator work with the default command-line-only interface. Mednafen GUI is a fine one available from SourceForge. Just drop both of the .exe's in the same directory, run the one that corresponds to the GUI program, and then it's a simple matter of clicking the "Open ROM" menu item.
Note: This link takes you to the vendor's site, where you can download the latest version of the software.