The following is a list of all dates and series letters as of 2015:
1862
1869
1874
1875
1875A
1875B
1878
1880
1886
1886
1890
1891
1896
1899
1917
1918
1928
1928A
1928B
1928C
1928D
1928E
1928F
1928G
1953
1953A
1953B
1953C
1963
1963A
1976
1995
2003
2003A
2009
2013
The first federally-issued $2 bills were printed in 1862. They were issued as United States Notes, a now-obsolete form of currency.
There were no series letters on 1929 bills, all of which were issued as National Currency bills. Please see the question "What is the value of a 1929 US 5 dollar bill?" for more information.
The last printing was in 1945. However these bills were issued as part of the 1934 series and they carried the series date 1934 A.
The vety first print
There aren't any US bills dated 1936. The special HAWAII-overprint bills issued during WWII all carry a 1935 date. Please see the question "What is the value of a 1935 A US 1 dollar bill with HAWAII on it?"
Three dollar bills exist but they were never issued by the US government, although the US issued a three dollar coin from 1854 to 1889. Earlier, some colonies printed three dollar bills. When banks were allowed to print money in the early days of the US, some printed legitimate, legal three dollar bills. The Confederacy also produced three dollar bills.
The first federally-issued $2 bills were printed in 1862. They were issued as United States Notes, a now-obsolete form of currency.
Yes. All US Dollar banknotes issued since 1861 are still valid.
Washington's portrait has been on all US $1 bills issued since the early 20th century.
As of July 2010 no series 2009 or 2010 $2 bills have been printed.
There were no series letters on 1929 bills, all of which were issued as National Currency bills. Please see the question "What is the value of a 1929 US 5 dollar bill?" for more information.
The US issued $1 bills and $1 coins with that date. Please see the Related Questions for more information.
The last printing was in 1945. However these bills were issued as part of the 1934 series and they carried the series date 1934 A.
Nothing. The US has never issued a million dollar bill. However, many businesses print fake million dollar bills for sale as novelties.
The vety first print
Yes, many millions of them. All US $2 bills were printed as red-seal US Notes from 1928 to 1963. Most $2 bills issued before that also had red seals but weren't necessarily US Notes.
Old US $1000 bills carried a portrait of President Grover Cleveland. Some privately-issued bills may have had a woman's portrait, though.