[Galaxy S III General] Ajdnet:
I am on stock 4.1.1 unrooted and get 5.5-6 hours on-screen time pretty constantly. My battery saving measures include:-

1 - Disable ‘Location Services’

2 – Deactivate Google Now (when in Google Now, hit the settings button)

3 – Disable S-Voice. Open the S Voice app, press the Menu button, then go into Settings & uncheck the ‘Open via the home key’ & Wake up Command. This will also give you faster access to the home screen because the phone won't wait for the second press to launch S Voice. Then Settings > Applications Manager > All > S-Voice > “disable”.

4 – Disable facebook app (SNS) via Settings - Applications – All, select app and then Disable.

5 – Disable S Suggest app (always live in Running Services, for Samsung app suggestions) via Settings - Applications – All, select app and then Disable.

6 - Disable Video Hub (always live in Running Services, for Samsung video purchases) via Settings - Applications – All, select app and then Disable.

7 – Disable Samsung Push Service which is always live in Running Services (Samsung Push Service is an application that sends you "push notifications" about apps and offers on Samsung Apps i.e. those that appear in the notifications bar with the Samsung Apps icon. You can uninstall it but every time you run Samsung Apps it reinstalls it). You can deactivate the service by opening Samsung App, Menu > Settings, uncheck "send push notifications". If you have any Samsung Apps installed (e.g. Polaris) you have to also disable the Samsung Push Service App via Settings - Applications – All, select app and then Disable (after uninstalling updates first, if applicable).

8 - Reduce background data and syncing. Set your various apps to manual syncing (or switch off your background data completely) to instantly extend your device's battery life by a significant amount. You can also deactivate notifications for each and every app you install in Jelly Bean. Go to its info page under Apps, uncheck the box labelled "Show notifications" and enjoy your empty notifications bar and also save battery.

9 – If a Samsung account is created, you can use Samsung Account sync de-activation: Go to Settings > Accounts and select Samsung Account. Select email address and untick anything you do not want to sync.

10 - Adjust widgets - Never forget to adjust your widgets! Having access to Facebook, Twitter and your favourite news on your home screen is great, but it tends to use a lot of power. Since widgets automatically update themselves in intervals, your battery can drain out pretty quickly. Do you really need to know this minute that your friend had salad for lunch? You can adjust widget update times by going to the settings menu of each app. Once there, hit the menu button> Settings> Notifications/Widget Update Interval. You can set the interval on most apps to a minimum of 30 minutes so you do not take up a lot of battery on updates. Most apps also allow for manual syncing.

To save even more battery, you can also download JuiceDefender to help monitor your Android’s battery. With these apps you can have an automatic tool that temporarily locks down the apps that take up a lot of battery. As a fan, I can tell you that they work great and are definitely worth a look.

For the long-term health of the battery, make sure to charge your smartphone often and don’t let your battery drain completely before you decide to plug it into the charger. Try not to let it get below 10 percent too often. You also may want to let it completely die about once per month. This is called power cycling, and it is very important to the health of a battery. Also, as much as you can help it, keep your smartphone at or close to room temperature. Do not leave it sitting out in the sun.

Hope the tips help!