How to Emulate Arcade Games on Your PC
The little Multiple Arcade Machine Emulator that could (and could really use a better acronym, too) turned 14 years old this past February, and it still isn't exhibiting much in the way of growing pains, though it continues to be distributed exclusively as a 20MB command-line app.
You're probably not going to like that, so I recommend instead that you obtain the MAME IV/Play GUI, which will make your life a little easier. Download MAME and the GUI, unzip both files to the same directory, and run the 'Play GUI' executable. It's nothing but a (long) list from which to select games, though it supports find-as-you-type.
You won't find much in the way of options in the GUI itself, which is mainly useful for browsing and loading games, but the program does a pretty good job on its own of booting up in a full-screen, scaled-not-stretched display. If that's not the arrangement you want, you can change it from the in-game menu (to do so, press Tab). Use the arrow keys, Enter, and Backspace to navigate; rinse and repeat.
Though there are a few reasonably good stand-alone Neo-Geo emulators, MAME supports every one of that system's games. You'll need to plunk a Neo-Geo BIOS in your MAME ROMs directory for any of the games to boot, but that process is actually a little less painful than usual, as some ingenious folks managed to reverse-engineer the thing a decade ago and now provide it for free as the "Unibios."