Ill tell you5 important reasons right now
1. remove all bloatware (find that thread somewhere here) speeds up phone significantly
2. Install "google now" i use this all the time way better than google search
3. GL To SD only works with root, meaning i can put HELLA GAMES on my phone (moves games from internal memory to sd card) when your games are like 1gb+ your phone fills up quickly and limits you from putting games (5gb Internal Memory), i got a 32gb micro sd, so i got GL TO SD and got hella games installed
4. Way more control if your phone goes bad u can use "CWM" and wipe your phone very easily sometimes if your on stock and your phone goes bad it still wont wipe completely. seriously why NOT root? I had to fix my girls phone that was the ONLY WAY i tried everything
5. Customization, CWM, Roms, new shit coming out, performance and audio tweaks, i means the list goes on just ROOT NOW