The original game engines (be it an arcade system, console or a computer) used anything from real FM synths to fake beepers with a touch of FM etc. Some later games even used lo-fi samples

As suggested already some of the simpler ways to get old video game-like sounds is by using VA synths as the front panel interfaces allow for quick access to most parameters. Even though most VA synths like the Microkorg and MS-2000 etc have a different synth engine to real FM synthesis they are quite capable of producing and faking most of the sounds you seem to be after.
Won't sound as authentic though...

IF you want the true arcade sound then stick to using the actual FM synths. Google for "FM Synthesis" and a few billion links would come up.

I must warn you that FM programming isn't as linear and easy as the all predictable, subtractive analog and virtual analog (VA( synthesis. The good news is that there are thousands and thousands of free sounds for classic FM synths like DX7, DX9, DX100 etc so the only thing you may have to do is browse through a few million patches and find the ones that sound like what you need.

Getting software FM synths like NI FM7 and FM8 is also an option. But I think that its a bit of an overkill for your needs. Although they are fantastic synths. Way way way easier to program than the original DX series by Yamaha.

I know this is a lot to digest but I also mentioned samples. Basically all the lo fi speech and bits of dialog (although not too many games from the 80's have that) are easy to re-create by using either hardware or software samplers and dithering the sample rate of sounds so the sound quality is just garbage. I'm talking 8 or 4 bit with lowest possible sample rates.

-ED-

[This message has been edited by 3351 (edited 10-30-2006).]