In The Hobbit, Bilbo Baggins stopped off at Rivendell with the dwarves on the way to the Lonely Mountain and also on the way back to the Shire with Gandalf.
In The Lord of the Rings, Frodo Baggins and his Hobbit companions journey to Rivendell, where they meet with Bilbo, who had retired there after his "Long-expected Party". Several other Elves, Dwarves and Men also arrive at Rivendell on separate errands; at the Council of Elrond they learn that all of their errands are related to the fate of the One Ring, and they must decide what to do about it. In the end it is the Hobbits who influence the decision.
The Sindarin name for Rivendell (which is probably a translation thereof) is Imladris, meaning "cloven valley".