The icons on the Samsung Galaxy S3 have large gaps between them, enough so that if they were moved closer together you could fit at least one more row and maybe one more column. Is there a way to change this?
This is what it looks like:
AFAIK there's no built-in method to achieve that personalization.
I would go with Apex Launcher by Android Does available from Google Play Store, to use with Android 4.0+, it's free and among the features you'll find:
APEX Launcher Homescreen Settings:
Other features can be found if you go PRO.