Hey, I may be in the same boat as OP. This is my first smartphone, so I can only compare my experience with other's. I use it ALOT, and my daughter plays games on it too. However, I have to charge it over and over throughout the day. I thought that's the way it's supposed to be, like when I use my laptop. Now I don't know. I got battery defender (which, from what I understand improves your battery life over time by learning how you use it), and Advanced Task Killer, which I use all the time, esp when my phone slows down. Seems to help some (would appreciate negative feedback on those apps).
You have a Galaxy Nexus correct?
From my understanding, Ice Cream Sandwich no longer has need for the "task killer" apps that exist in the market. It manages apps on it's own and each app will either have an "exit" option, or you simply escape out of it, and ICS will idle the app.