Green Power is the app for me. Manages my wifi, data and sync times beautifully on my SG3. Has improved my average battery life to 19 hours after an average day's use.
I'm wondering if I'd see that kind of improvement. I've had mixed results with battery saving apps. However, I do see Green Power getting a lot of good reviews.
As for things I absolutely love on my phone...Voxer, for talking with friends without burning minutes. It's like the best part of push to talk with message services. Pretty handy. Also, Groove IP (paid or free, paid has better sound tweaking capabilities) for making Google Voice calls over wifi. Handy if you burn through minutes of a plan, or like me, experience intermittent coverage where you live.
Half of my phones life is wifi.
Keyboard right now is SwiftKey 4, which I'm loving. It's the first predictive swyping text keyboard that actually seems to say what I'm trying to say.
Cam Scanner has been a lifesaver for me. Between that and online printing services, I don't really even need a scanner/printer anymore. Scan to .pdf, image file, etc. Handy as could be.
Talk To Me Cloud is a fantastic app for languages. I live close to Mexico, and my Spanish is so/so. If I have any kind of data though, I can get by with this app. Speak, get translation. Nuff Said.
Last but not least, Wifi Tether for root. Forget paying 15 dollars a month. Pssshhhhhh.