Depends on your definition of poverty. Poverty in the sense of the aforementioned grandparents has - only a fraction of a % of the population of the US lacks indoor plumbing.
In the US, people with earned income < $5k/year still tend to consume $23k/year.
We have an organization here in the UK called the Joseph Rowntree Foundation, who lobby on poverty and publish statistics, but they use a relative measure of poverty as basically, being in the bottom third of the population. So, if your next-door neighbours on both sides are watching Blu-ray and you have a lowly DVD player, then they would count you as "living in poverty" for the purposes of the statistics they compile.
When you consider that the very poorest in the UK have free housing, welfare, free education and healthcare, etc, then "poverty" in a global sense is very obviously long since eliminated here.
In the US, people with earned income < $5k/year still tend to consume $23k/year.
ftp://ftp.bls.gov/pub/special.requests/ce/standard/2009/income.txt
By the standards of the past, poverty more or less has vanished. We just raised the bar for poverty so that we have someone to feel sorry for.