I have my own ideas about the order of importance of the great hobbit deeds... I ordered them by what I believe took the greatest courage and strength of character in each of the given circumstances. Accordingly, there are some things left off from the previous lists. I also tried to limit the list, because while there are many great hobbit deeds worth mentioning not all fall into the category of brave or notable deeds, which was the original topic.
1 - Frodo's efforts to destroy the ring.
- Easily the most notable hobbit deed of all time and requiring the greatest strength of character.
2 - Bilbo surrenders the ring before leaving Bag End.
- Bilbo may not have known what the ring was, but he used to wear it for weeks at a time--its hold on him was very great.
3 - Sam's efforts to help Frodo destroy the ring.
- I think the Bible says it best, "Greater love has no one than this, that someone lay down his life for his friends," and Sam knew well that the quest was likely to end in death.
4 - Bilbo gives the Arkenstone to the men of Dale.
- To do what one believes is right when it may cost them everything, especially high-standing in the minds of others, is a quality rarely found anymore in the world.
5 - Sam rescues Frodo from Cirith Ungol.
- Sam chooses love and friendship over all fear and the pull of the ring, and braves the tower.
6 - Bilbo rescues the dwarves from giant spiders.
- Risking his life for dwarves who still don't think him all that worth their time, and doing part of it without invisibility.
7 - Merry helps slay the Witch-king of Angmar.
- An act of great courage despite his knowledge of the great personal risk.
8 - Pippin slays a troll outside Morannon.
- Just like Merry (and interchangeable I think in ranking) an act of great courage despite the risk to his own life.
9 - Bilbo confronts Smaug.
- Facing a dragon alone requires a lot of courage and character, but not as much as if one didn't have a magic ring.
10 - Sam defeats Shelob.
- Taking on this giant spider requires great courage, but not perhaps as much courage as others would need to complete the task--I think it's fair to argue Sam is the most courageous hobbit in history.
11 - The hobbits take back the Shire from Saruman.
- A group effort so not as high on the list, and probably seeming like nothing after everything else they had been through. But still notable and courageous.
12 - Bilbo gets the dwarves out of Thranduil's realm.
- Perhaps deserving of a higher place on the list, but we know by now of Bilbo's propensity to pop his ring on and disappear if danger was near to him.
13 - Bandobras Took slays Golfimbul at the Battle of Greenfields.
- Orcs are quite frightening whether you are a halfling or one of the big-folk. But he was four foot five and had a horse.
14 - Frodo decides to go to Mordor alone.
- At this point Frodo had some idea of what he was getting into so it was a very brave decision, but he didn't yet know the great weight the ring would become.
15 - The hobbits continue on the quest after their encounter with the barrow-wights.
- A new one, and last on my list. For the four hobbits to be willing to strike out on their own without Tom Bombadil after near-death is quite notable and brave, but they still were very innocent.
Now you may ask...why didn't I include Sam giving the ring back to Frodo? Or Lobelia confronting Saruman, or Frodo defying the Nazgul, or any of the other things previously mentioned? Well...
In the case of Sam returning the ring, I believe he had already made that choice in his heart before he had even found Frodo. His heart was not with the ring but with his friend, and that wasn't going to change. Which is also why I might argue that Sam has the greater strength of character between the two of them, but that's another topic.
Other items I left off were either because they made the list too long and were about the same level of courage and character as other things (much like Merry's and Pippin's individual deeds). And then there were other deeds that were noteworthy but not falling into the categories of brave, courageous or requiring strength of character. Some in fact are mere historical facts or instances of happenstance rather than requiring any character strength on the parts of the hobbits (such as Gollum's accidentally falling into the Cracks of Doom with the ring).
That said, there is one such deed in hobbit history I wanted to bring up because I find it is often forgotten: Marcho and Blanco get permission from Argeleb II to cross the Brandywine and begin settling the Shire. It may not necessarily be courageous or even notable outside that it is the beginning of recorded hobbit history, but without them it can be safely said our dear hobbits of the Shire wouldn't even exist!
So that is my list. A humble noob, I welcome your comments!