i've had Galaxy S 1 for about a year now and this is how I get my game fix:
1 - T store has a good selection of free games, a lot of them are Korean though, but some are in English
2 - there's an app called My Market which gives you unrestricted access to apps in other countries and also lets you download games for free sometimes...not always though
3 - if you are able to get apk file from elsewhere, you can usually install it manually using the Android installed app and KIES software or I guess you could just use ASTRO and do it directly from your phone. i don't do this anymore tohugh because torrents never have any good new games and it's very time consuming to install them
4 - if your phone is rooter, use the market unlocker, like someone suggested and you can then install directly from the market or, better even, AppBrain, which has games that were removed/not available on Market. with appbrain, you can get some really awesome games for free and sync them all at once in a second.