The Neo Geo was made by SNK in 1990 and was used for over 15 years even after SNK went bust. There are two versions of the machine, the MVS (arcade) and the AES (home console). While most of the time the arcade ports are perfect in a literal sense since it was on the same hardware, sometimes there were censorship or minor changes done for the AES version. A lot of fighting games were on the Neo Geo however there are some from other genres too such as shoot em ups, beat em ups, sports games, run and gun games, even Bomberman.
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MAME has been able to run Neo Geo games for years and over the years, MAME became more accurate with the machine too. The default is the MVS version however it is possible to run the AES versions with some extra work (since MAME itself is like the Neo Geo as in that it can run arcade and console games too). It doesn't support the tile viewer.
Not as accurate as MAME and is no longer supported meaning that it might get harder to run on modern computers or finding ROMS. Still it has sprite ripping features and it is easier to boot up the AES version of a game too.