"Rufus is a man of action and, having fought Dark wizards for most of his working life, does not under-estimate Lord Voldemort."
-- Albus Dumbledore (HBP4)
Scrimgeour took over at a dangerous time, when the return of Voldemort had been revealed and the Wizarding world was in turmoil. Scrimgeour was a warrior and took the threat of the Dark Lord very seriously indeed, but his approach to the situation was not all that different from that of his successor. He created new bureaucracy and printed warning pamphlets and, when quick successes didn’t happen, arrested innocent people to make it look like he was doing something (HBP3).
He pestered first Dumbledore and then Harry to get “The Chosen One” to be seen supporting the Ministry, thereby bolstering its image in the public eye. When Harry wouldn’t cooperate, Scrimgeour became angry and said that it was time the boy showed some respect. Harry responded that it was time Scrimgeour earned it (HBP16).
Scrimgeour was described as having a leonine air about him. His tawny hair had streaks of gray in it. He wore wire-rimmed spectacles and walked with a limp (HBP1).
Rufus Scrimgeour is possibly related to Brutus Scrimgeour, but this is not confirmed as canon. The surname, however, is not very common in Britain, so it is more likely than not (British Surname Distribution).
Harsh, persistent leader, former Head of the Auror Office
Rufus is Latin for "red-haired" (Behind the Name).
Rufus Scrimgeour is played by Bill Nighy in Harry Potter and the Deathly Hallows Part 1 (IMDb).
Lexicon list of Ministry of Magic employees
From the Web
Writing by J K Rowling on Pottermore: Ministers for Magic
Pottermore feature: Rufus Scrimgeour
Harry Potter Wiki: Rufus Scrimgeour