What did the new Doctor Who do to date?

Answer 1

Quite a lot of things, actually. Assuming by "new" you mean Matt Smith, he, in order of his relative timestream,

-Saved the world from the Atraxi

-Helped to end the torture of the Star Whale aboard the Starship UK

-Stopped Daleks from destroying WWII London

-Stopped the Weeping Angels from taking over the universe

-Saved 16th century Venice

-Helped to create a ceasefire and eventual truce between the Silurians and humans

-Saved Provence and helped van Gogh with his self-esteem

-Saved Earth from an out-of-control time engine

-Rebooted the Universe after it crashed due to an exploding TARDIS

-Saved a galactic space liner from crashing into a planet

-Rid the Earth of the Silence

-Saved 17th century pirates from an alien Siren

-Saved the TARDIS from the malevolent being House

-Brought a new understanding between humans and the Flesh

-Saves River Dong from Madame Kovarian (twice) and saves accidentally saves Adolf Hitler from assassination by an alien cyborg

-Teaches an alien boy named Alex snd his previously ignorant human parents how to coexist and adjust

-Saves companion Amy Pond from a kindness centre on Apalapucia

-Saves a space hotel from a too-old minotaur

-Saves the Earth from Cybermen

-And repairs the damage done to the time and space by a well-meaning River Song, and marries her