Here you see me making mario jump over the flagpole on level 3-3, it is also possible to jump over the flagpole in level 7-1.I have also seen videos of people doing it on level 1-1, but they cheated and used tools that made them able to do it.
From Wikipedia:
is a 1985 platform video game developed by Nintendo, published for the Nintendo Entertainment System as a sequel to the 1983 game Mario Bros. Learn about Super Mario Bros.