Before I say anything, I just have to say that improving battery life is not a good reason to root your phone, and you will most likely be disappointed by any battery performance gains from other ROMs. Most of the time, battery drain on custom ROMs will be worse than stock ROMs. When it comes to jacking up the battery life, like others have said, your best friend is keeping the screen brightness down. Switching wifi off when you're outside your house is also a big battery-saver.

There are, however, many great reasons to root. You can access all of your phone, you can do things like changing the boot animation, adding boot sounds, changing the partition layout, adding extra security features... the list goes on. My two favourites are the Xposed Framework (lets you customise your Android in crazy ways without messing with cumbersome and dangerous system files) and Titanium Backup (backs up all your apps and data and lets you restore everything when you flash a new ROM).

Rooting your phone is fun and harmless, IF you make sure you understand a few things about your phone first:

1. You know what your carrier is, and whether you are using a CDMA or GSM network.
2. Using the previous point, you know which ROM/version of the ROM you need to flash to your device.
3. You know whether you want to go stock Android (AOSP) or an OEM skin like HTC's Sense or Samsung's Touchwiz.
4. You understand whether you need to upgrade the radio or not (99% of the time NOT, but messing with your radio is one of the few things that can brick your phone even after rooting).
5. If it's the first time the phone is to be rooted, you need to be clear on what you need to flash and in what order. Usually it goes like this:
- Unlock bootloader
[- S-OFF your bootloader IF required (and if available for your device), usually it's a convenient but not completely necessary step.]
- Flash recovery
- Flash superuser zip via recovery.
6. If you want to go on and flash custom ROMs, it goes like this:
- Perform a full wipe of the device
- Flash kernel if you didn't S-OFF the device.
- Flash ROM
- Flash gapps
- Wipe cache

tl;dr: Rooting won't save your battery, do it anyway.