You can edit the gtk-main.css
or nautilus.css
files.
I recommend you to try this under your ~/.themes
and not system-wide. You may either change the background color of nautilus only or the base theme as a whole, which affects a lot more programs. In this example I will change the background color in the default Ubuntu Theme "Ambiance" (in Ubuntu Gnome use the folder Default instead) from white (#ffffff) to a light grey (#D8D8D8). Feel free to pick any other color.
For comparison how it looks like in the beginning:

Create a copy in ~/
Create your ~/.themes
directory and copy the original Ambiance theme to it.
mkdir ~/.themes
cp -R /usr/share/themes/Ambiance ~/.themes/
Change the background color for the whole theme
If you want to change the base color for the whole theme, edit the base_color (Hex notation #??????) in gtk-main.css
. This changes the background color of other applications (eg: gedit) as well.
nano ~/.themes/Ambiance/gtk-3.0/gtk-main.css
Change this line:
@define-color base_color #ffffff;
For this one:
@define-color base_color #D8D8D8;
To save the changes in nano, press Ctrl+O,Enter then Ctrl+X.
Effect:

Change the background color for nautlius only
If you want to change the background color for nautilus, edit nautilus.css
.
nano ~/.themes/Ambiance/gtk-3.0/apps/nautilus.css
Add this lines to the beginning of the file.
NautilusWindow * .view {
background-color: #D8D8D8;
}

To save the changes in nano, press Ctrl+O,Enter then Ctrl+X.
Effect

To see the changes you can restart nautilus, logout login or restart your machine.
Best Answer
There are 2 options which resemble Mac OS very closely, both designed from similar code
Update This is a duplicate question.
UPDATE 2 I tried both Marlin and Pantheon Files (from other Stack Exchange contribution, see below). It seems that Pantheon files makes it easier to switch over from Nautilus. I am using Ubuntu 12.04 LTS.
It is called Marlin File Browser
Installation of Marlin
Option 1: Marlin with Dropbox / Ubuntu One support
Option 2: what I have tested without dropbox/ubuntu one support
According to the website, it is rather new and might have issue. Check out this article with some nice pictures showing how similar it is to Mac OS X file and folder color labeling.
Also, see this article for how to install it on Ubuntu 12.04 or 11.10 or on Linux Mint.
Installation of Pantheon File Browser:
For Dropbox or Ubuntu One support, add the plugins: