Battery failures have been very rare in any hybrid and the manufacturers (Honda and Toyota) have been very good about backing them up at little or no cost to the owner. There are some symptoms you can look for that would indicate a weakening traction battery:
1 - You MPG will slowly drop with no other explanation.
2 - If you can determine the State-Of-Charge in you HCH (It is displayed in a Prius), put a known electrical load (I use my Thermoelectric cooler - 4 amps at 12 v) on the car in ready mode and see how quickly the SOC drops (the engine should start to recharge it as required). If the battery is weakening, the SOC will drop faster under the same conditions.
Your battery should last longer than many of the other components of your car. I expect to go more than 200,000 miles in my Prius (2004 - 64,000 miles to date) without seeing appreciable degredation.
There have been no reports of dying batteries on Honda or Toyota products. The manufacturers expect them to last the useable life of the car.
Keep in mind that your battery is backed up by a 8 year / 80,000 Honda (100,000 Toyota) warranty and, if you are lucky enough to live in one of several states which have special PZEV laws, a 10 years / 150,000 mile warranty.
This is longer than any other component in the car.
The only hybrid for which I've really heard of battery failures is the early Insight, which was Honda's first so there were a few hiccups with the battery management. That said, the most commonly reported symptom that I've read about is frequent recals, during which the battery SOC drops precipitously and then is force charged. It seems that if that happens with increasing frequency, you can expect an IMA light which will indicate system problems and probable battery replacment. Keep in mind that this is not personal experience, but information I've gleaned from spending far more time than I ought to surfing this and other forums.
Jordan, you won't. The warranty "enhancement" only takes effect if you buy from one of the CARB states, and possibly if you live there as well. So I can't, for instance, jump over to NY to buy my car and expect the better warranty when I actually live in, and will get tags from, Ohio.