Android always allow apps to start automatically and run under the background. Except few, all Android apps consume constantly CPU and drain battery for nothing. Greenify by Oasis Feng comes to rescue, it freezes these bad guys while they are not working for you. Now my S4 drops only 1-2% battery overnight with MailDroid and WeChat pushing turned on and Acrobits connected!
I add almost all apps into the hibernation list, except aforementioned MailDroid, WeChat and Acrobits. Greenify is quite smart, it won't hibernate an running app if it is indeed serving me, such as OpenVPN, Touchpal and MortPlayer. Boat browser (not the mini) is the only app I don't let Greenify freeze it, because it does not always consume CPU like other browsers and it is a hassle to reload a page each and every time while Greenify waking them up.
The paid version can also freeze system apps, but I'd rather remove them instead and, if needed, reinstall them (not copying them back to /system/app) as non-system apps.
GMail can be greenified and push will still work, because push is not handled by GMail app itself but by system service that will open up GMail when a message arrives, even if GMail is hibernated at the moment. This comes to the grace of Greenify - it does not disable an app, it only pauses it and keeps it available.
Google Voice, on the other hand, handles push by itself and should not be greenified if you don't want to miss your GV SMS and VM.
It is great to see such great apps developed by great Chinese developers! ES File Explorer is another great one. Wish many other Chinese developers of PPS, iFeng, LeTV... will learn to behave themselves.