Having heard that Sylvester McCoy is slated to play the role of Radagast the Brown in the upcoming film adaptations of "The Hobbit", I am wondering what role this character actually plays in those events?
Like Legolas, Radagast doesn't actually appear in The Hobbit, although he is mentioned briefly by Gandalf and is a friend of Beorn who does appear. The upcoming movies are based- somewhat loosely perhaps- on both The Hobbit and the intervening period before the opening of The Lord of the Rings, so Radagast may play some role at Dol Guldur or other wizardy events which are not explicitly covered in The Hobbit.
Radagast is a member of the White Council. During Bilbo's adventures Gandalf leaves Thorin's party at the border of Mirkwood as he has been summoned to a meeting of this Council. This meeting decides to, in alliance with the elves of Lothlorien, go to war to drive The Necromancer (Sauron) from his stronghold in Dol Goldur.