[Galaxy S III General (US Carriers)] elterible:
I posted a similar guide for my Galaxy SII, so I figured I would share the love here. Hopefully this helps out a few folks who want to better utilize the amazing screen on the GSIII. Please feel free to comment and make suggestions and please "thank" if you appreciate the post!

General Info for Beginners:

The Galaxy SIII comes with a gorgeous 4.8 inch, 1280 x 720 (albeit pentile) screen. As great as the screen looks, I couldn't help but feel that there is a lot of "wasted space" at the existing resolution. The best example of this fact is the app drawers default 4 x 5 layout. In my opinion, things look much better when the the icons are a bit smaller and more tightly grouped. For those that feel the same way, there is a simple build.prop edit you can do to "trick" you phone to thinking it is set to a higher resolution

How-To Change the Density Setting:

To accomplish this, all you have to do is change the build.prop setting for "ro.sf.lcd_density". There are multiple programs out there that makes this much easier but I have found the best results with "ROM Toolbox". Feel free to buy the full version to support the dev but if all you are looking to do is change the density setting, the lite version will do just fine.

1. download and install "ROM Toolbox" from the Google Play Store

2. go to the "Performance" tab

3. click "build.prop tweaks"

4. change the "LCD Density" slider to whatever DPI you like

5. reboot

As mentioned, there are multiple programs out there but based on my personal experiences, DO NOT USE "LCD DENSITY MODDER" from the play store. This app is known to cause soft-bricks/bootloops. However, I have been told that LCD Density Modder CAN still help with the Play Store app issue, but you will have to buy the pro version for that feature. Thanks uber_mike! (more on that later)

What Setting to Choose:

This is matter of personal opinion so try out different setups and see what you like best. Remember, the lower you set the number, the smaller your icons/text will appear but will also give you more screen real estate. I suggest starting from about 280 or so and working your way down and find something you like.

You may also notice that text and icons appear less sharp when messing with these settings. Keep in mind that because you are not truly changing your screen resolution, the translation will not be perfect. Personally, given the natural sharpness of AMOLED screens, I think most people while not be bothered by this or even notice.

"Phone Mode" vs "Tablet Mode"

As some posters have reported, going to 240 dpi or below will result in Android thinking your device is a tablet. I have been running 240 for a few days now and I'm loving it. In my opinion, may apps look a lot better in Tablet mode but if there are certain phone only apps you MUST have, please keep this in mind.

Potential Issues and Workarounds:

You will inevitably run into some compatibility issues so here are few final thoughts

Which ROM to use?

TouchWiz-based Roms: All roms based on stock Samsung TW for the GSIII were written with only the native resolution in mind. This means that certain apps and aspects of the OS will not scale well with a higher resolution::

- TouchWiz UX Launcher: If you are dead-set on using the default TW launcher, this mod may not be for you. The proportions will look way off and because you cannot edit things like margin or grid layout, it is not fixable. Aftermarket launchers like Apex handle the conversion much better (more on that later)

- The Phone Dialer: The dialer looks like small box that fills up only a portion of the screen. To resolve, you can use an aftermarket dialer app like "exDialer" from the Play Store

- TW E-mail App: The TW e-mail app (not gmail) also doesn't scale well. You can flash the AOSP version of e-mail as a workaround

- Stock Camera App: You will notice some of the border coloring and margins doesn't scale very well but the functionality is still perfect

- Notification Bar: I have noticed the little lines in the pull-down become off-center after you adjust the dpi. Again, a minor annoyance which doesn't effect functionality

- Twitter:*You may have profile pictures show up in 2 different sizes (Thanks Msilvame!)

Some additional feedback from other posters(thanks mhtruth!) but note that I personally do not have all of these issues

*status bar quick toggles DON'T scroll (stuck with just the 1st 5)

*status bar "remove all (X)" missing (swiping still works)

* in call speaker boost doesn't work...(only stops you from hearing not the person on the other end)

* some apps go into tablet mode (ex. HBO GO)

AOSP ROMs: CM9 and AOKP handle the conversion a bit better. You won't run into the dialer or e-mail issue like with TW ROMs but there are still some bugs. I realize there are not any AOSP Roms for the GSIII yet but this is based on my experiences from my GSII

Update: looks like we have CM9 Nightly's now!

Update 2: and now we have AOKP! Thank you devs! FYI, I've been running AOKP since last night and it's working great, not a single bug

- Certain pictures of contacts may appear too zoomed in, i.e. messaging notification pictures or the favorites tab

- Other aspects of the OS may become hard to read when scaled down so much, i.e. lock screen add-on buttons, notification pull down buttons

The Play Store Doesn't Show All Apps?

- This is the biggest pain in the a$$ when you mess with the lcd density settings. There is a bug in the play store that prevents you from seeing certain apps when you change the lcd settings away from default.

I have seen a few "hacked" versions of the vending.apk out there that makes the play store think you are always set to a stock dpi but for some reason, this only works for a little while. LCD Density Modder Pro has a feature where it can install a "fixed" Play Store app that can help with this issue also, but there is also a workaround.

Here are the steps to get the market working again:

1. Change LCD Density back to stock (320)

2. Reboot to take effect

3. Clear the data for the Google Play Store AND Google Services Framework

4. Open the Play Store app and you should see everything again

5. Change LCD density back to whatever you like.

6. Reboot

I know this is a bit cumbersome but it's the best solution for now. I haven't quite nailed down what triggers the market to "break" but hopefully you won't have to do this fix too often. In opinion, this small annoyance is worth it.

Also, one thing I noticed when using Rom Toolbox is that after you set your dpi to a lower setting using the "build.prop tweaks" menu, if you go back and try to set it to the stock 320, it will max out at 280 or so. Not sure why this is the case but to do this manually, go to "build.prop editor" instead and change the "ro.sf.lcd_density" to 320.

I have been told that setting your dpi to 240 will also help with Play Store issues, since 240 is a stock resolution on other devices (GSII comes to mind). Feel free to try this out, but the size of icons and fonts may be a bit too small for some tastes (thanks DutchDogg54 and chakra!)

Everything Looks Too "Stretched Out"?

- Having an aftermarket launcher will help with this tremendously, as the TW launcher does not scale well at all. I personally use Apex Launcher and there are some settings you can change to make the proportions look better

1. Homescreen Settings: Change the Vertical and Horizontal margins to medium or large

2. Dock Settings: Same as above.

You may also want to mess with different homescreen grid configurations now that you have extra room. I have bumped up mine to 5 x 5 and it looks great.

Bumping up the font size can also help even things out. At 260 dpi, I put mine to "normal", but at stock I used "tiny" (thanks falconator!)

List of all the ICS compatible launchers that will work for this mod:

- Apex Launcher (my fave)

- Nova Launcher

- Go Launcher

- Stock ICS Launcher / Trebuchet Launcher

- Atom Launcher (new!)

And that's it. I hope this will help you out so that you won't have to go through all the trial and error I did. I promise you, after you do this, it will be impossible for you to go back to the stock resolution (everything looks HUGE)

Update: I have added some of my and mhtruth's screenshots for those who are interested. I also added a screenshot of HBO GO in tablet mode

My setup:

- 240 dpi (Tablet Mode)

- Team Sonic Free GS3 Rom (R3)

- Apex Launcher with kovdev ICS Theme

- Homescreen: 6 x 5 grid, Horizontal Margin: Medium, Vertical Margin: Large

- Dock: Horizontal Margin: Large, Vertical Margin: Medium

- EX Dialer and Contacts (for better scalability)

- Font Size: "Normal"

- "Enhanced Email" App (need it for exchange access)

Feel free to show off your own homescreen screenshots! I will update OP and add yours too!