Is it possible to get the Samsung Nexus OS on a Galaxy S3?

Welcome jnguyeen! I am not clear on what you mean by the OS? You mean the Android version such as IceCream Sandwich or JellyBean version?
I am not sure on what version the Nexus has, but is it the way it looks that you like or the options that it has?

 

Another welcome to the site, jnguyeen

I hope my esteemed colleague Mikestoney doesn't take this the wrong way, but I think I understand what you really mean. The Samsung Galaxy Nexus is a developer type phone, meaning it usually ships with (and runs) a more "vanilla" look of any version of Android as oppposed to the GS3. This means that you _might_ see less perceived 'bloatware'. And as such it is easily rooted and ROM'd.

Anyways, before I assume to much, you could look into rooting and installing a custom ROM on your device which is free, but can be pretty 'techie' demanding, especially for your device. I suggest you go ahead and read through this section here:

Samsung Galaxy S3 - Android Forums

And see if there's any more info there for you. Rooting and most custom ROM's, when available for your device, provide the same type of experience as the stock Galaxy Nexus.

good luck

 

And if rooting your device and putting a custom rom sounds like too much of a headache and all you want is your phone to look aesthetically like vanilla android, you could always use a different launcher like nova launcher from the play store.

 

ICS also allows you to disable apps; I've got a bunch knocked out on my S2!