The largest bill you can get in the US from a bank is now $100. Until 1945 the US printed $500, $1000, $5000, and $10,000 bills for general circulation; there was also a special $100,000 bill made in 1934 and 1935 for transfers between Federal Reserve banks.
Distribution of high-value bills was halted in July 1969 by presidential order in an effort to combat their use in criminal activities.
If there are any high-value bills in circulation they are still legal tender, but banks will take them out of circulation when they get them. If you have one it's probably worth more to a collector, so it would be much better to sell it privately versus taking it to a bank which is only allowed to exchange it at face value.
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It depends on the definition of "biggest". If you mean by denomination, the winners include a bill denominated at 100 trillion (10^14) Zimbabwean dollars, and a 1924 German banknote from the Weimar Republic that carried a similar number of Marks. However both of these bills were issued during times of hyperinflation so their actual purchasing power was quite small.
Today one of the bills with the highest purchasing power is the EU's €500 note, equivalent to about US$600 in mid-2015.
During the mid-1930s the US printed bills with a denomination of $100,000 but these weren't put into general circulation; they were only used for interbank transfers.