Strictly speaking, the RTGs will continue generating power past that time -- it just won't be enough to power any of the instruments or the radio; the thermocouples also degrade, which further impacts the power produced. (tomato, tomahto) Attitude propellant is also an issue. Around 2020, they'll start to turn off instruments until they don't have enough power to run any of them anymore. Apparently, they haven't picked the shutdown order yet -- but they have 10 years to decide, so no rush. =)
Neat idea, but I don't think there were any onboard batteries -- AFAIK power was just fed straight from the RTG thermocouples, more or less. Batteries would have just added weight, would have had a crappy recharge capacity after a while, and wouldn't have made much sense for a deep space probe which relied on an RTG instead of solar panels.
Also, the RTG might be powering instrument heaters, keeping them at warm enough temperatures to prevent failure. If that's the case, once those are shut off, there's no turning those instruments back on.
NASA's timeline for the Voyager lifetimes: http://voyager.jpl.nasa.gov/spacecraft/spacecraftlife.html