Why can Bilbo, Frodo and to some extent Gollum resist the Ring's influence to a greater extent than men? What is the significance of this?
Looking at this from the aspect of your comment (“why did Tolkien choose to create hobbits without these character traits?”) on @Andomar’s answer (which actually includes evidence from the books — reward it with upvotes, readers), one of the themes of Lord of the Rings is the idea that the smallest, humblest person can change the destiny of the world, and become a hero.
The Hobbits represent small, humble, ordinary people. They don’t lust for power or fame, or aspire to do great deeds. Thus the Ring can’t corrupt them in the way that it would corrupt Boromir or Galadriel, although it can make them covet it as a possession.
This might have been inspired by Tolkien’s experiences in the First World War. The folk with grand ambitions and a lust for power seek terrible weapons to dominate the world, and the ordinary folk are forced to go to war and suffer as a consequence. To quote Harry Patch, and/or Radiohead:
Give your leaders each a gun and then let them fight it out themselves
Dwarves were even more resistant to rings. Sauron couldn't control dwarves who wore a Great Ring. The Dwarf's life was not extended, and he did not become invisible. From The Silmarillion:
Seven rings he gave to the Dwarves; ... The Dwarves indeed proved tough and hard to tame; they ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows.
All a ring did was amplify the Dwarf's bad character traits, like lust of gold.
While a Hobbit's life could be extended, a Hobbit (and especially Bilbo and Frodo) does not have many bad character traits that the Ring could work with. But the Ring overcame Frodo in the end:
'I have come,' he said. 'But I do not choose now to do what I came to do. I will not do this deed. The Ring is mine!' And suddenly, as he set it on his finger, he vanished from Sam's sight.
A Dwarf would not have been overcome like that. But Dwarves are not very good at sneaking. That's why Thorin was looking for a Hobbit in the first place :)