As previously mentioned, he's naturally a ginger, but dyes his hair dark brown for most of his roles (including Hawking), black for roles like Sherlock and Harrison, and a sort of dishwater-blonde for Tinker, Tailor, Soldier, Spy.
For Third Star he opted to lose a ton of weight instead of shaving his head (which he was growing out for Sherlock) in order to look like a sickly and emaciated cancer patient. He kept the appearance for Sherlock Holmes, who is known for prioritizing work over food.
Despite having a wig, he still dyed his hair platinum blond to portray Julian Assange in The Fifth Estate. He also wore contact lenses and false teeth for the film.
To make his voice deep enough for Smaug in The Hobbit, he literally tore into his vocal cords.
Fan Nickname: He has loads of nicknames. Some given by the press, others by fans, and even more from his own friends.
Tumblr has a particular fondness for "Baritone Gingerbatch". A notable one is Bandersnatch Cumberbund, which was from an article that unfortunately couldn't spell his name correctly and, simultaneously, had many fans poking lighthearted fun at his difficult name.
And the priceless one given to him by his schoolmate, which he disclosed on Alan Carr's talkshow: Bendy-dick Cum-on-my-baps.
"Butawhiteguy Cantbekhan" gained some popularity even among fans in regards to his casting in Into Darkness (which no one really blamed on him).
"Shezza", from the Sherlock episode "His Last Vow".