I thought I'd share this here since no one else has posted anything for the S4 yet. This is an easy guide to root your S4.

All credit goes to galaxys4root.com (naturally). This guide worked well for me. Keep in mind, there is one step that you don't need and that is, you don't need to put the SuperSU file on your phone. The CWM has a root option that works perfectly, so just select the root option in the menu. As I said, I tried it with my I9500 and it worked.

I9500 Exynos Octa-Core

(Also AT&T SGH-i337, and Sprint SPH-L720 supported using CWM root method, use CWM method if you are going to install custom ROMs)
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For GT-i9505, T-Mobile Galaxy S4 SGH-M919, Sprint Galaxy S4 SPH-L710, Canadia Galaxy S4 (Bell, Rogers, Telus), US Cellular Galaxy S4 SCH-R930 root method
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