You can emulate most of these games released before 2002 with MAME (Multiple Arcade Machine Emulator). Some games (Capcom, SNK) run better on WinKawaks and/or FinalBurn Alpha Playstation/Namco-based hardware runs better on ZiNc. NAOMI and NAOMI 2 games can be emulated in Demul, nullDC and Makaron, with varying compatibility. Nebula also has additional optimization for SNK, Capcom, Konami and PolyGameMaster systems, as well as the Sega Model 2 Emulator.
Protip: full MAME sets can be found at Pleasuredome.