It is said that the One Ring has a will of its own and can perform certain actions impossible for inanimate objects, most notably losing itself from Gollum to Bilbo. In hindsight, you could say that it had terrible judgement, since it indirectly placed itself in the possession of its destroyers.
I vaguely remember the Ring exercising its will at many other points in the books though. At which points did the Ring do so, and what actions were these?
As Gandalf says, "The ring wants to be found. It wants to return to its Master". Hindsight is always 20/20. Whatever may have been the final outcome, the ring was only exercising its will in order to be found and return to Sauron. This is seen several times when Frodo is "compelled" by the ring to wear it, so that Sauron's Nazgul can track Frodo and the ring.
Also, landing in Bilbo's possession might have been the ring's effort to not get lost (and thus ultimately be found). Staying in a household hobbit's possession has much better chance of coming to the limelight than staying with a wandering recluse.
The will of the ring seldom manifests in concrete actions and happenings, but more often in making its will into the will of the wearer. The wearers want to preserve the ring, all the way up to killing for to keep possession of it. This is the will of the ring since it wants strong people to wear and protect it. Frodo has a very hard time letting go of the ring, showing that the will of the ring has indeed been exercised throughout the journey (and, therefore, the books).
Another example is Boromir who is influenced by the ring and compelled to take it further towards Mordor. Perhaps the ring had then found that its current wearer had a strong will to destroy it and therefore tried to switch wearer. Failing this, the ring instead focused its efforts on corrupting Frodo.
The ring can only do what a ring is capable to do: change his size and weight. Bilbo was clever enough to put a chain through the ring, so the ring is not capable to escape anymore.
The actions where the ring influenced the wearer (I have only the German version of LOTR, so I do not cite them. You are free to edit and add citations).
Bilbo:
Bilbo put the ring into an envelope, addressed it to Frodo and intended to leave it on the mantelpiece. Suddenly he put the envelope in his pocket and is astounded later that the envelope has changed the place.
While Bilbo was extremely resilient he acknowledges that the extended lifespan does something negative with him: a feeling of etiolation.
Bilbo extended resistance to give up the ring. It is very probable that the ring sensed that Bilbo goes on voyage and tries everything in his might to influence Bilbo. The last influence is that Bilbo hand twitch involuntarily and the envelope sails to the ground.
Frodo:
Frodo wants to give Gandalf the ring but the ring increases his weight as much as possible to prevent Gandalf from getting the ring.
Frodo tries to destroy the ring during the meeting with Gandalf by throwing it into the hottest place in the fireplace and realizes that he is not able to do it, in fact, the ring forces him to put him back into the pocket.
Every time he meets the black riders he gets a very strong urge to put on the ring. The ring knows that the riders are allies and tries to force Frodo to reveal himself (Invisibility is not working with the riders).
In the Prancing Pony Frodo suspects rightly that the ring forced him to use him during his dance because there were strange men which immediately left after his disappearance.
During the attack of the black riders on the Weathertop they and the ring together forced him to use the ring to finally reveal himself.
During Bilbos meeting in Rivendell when Bilbo requested to see the ring, he felt besides his own feeling of amazement and distress resistance, a shadow fell between them and he saw Bilbo as repugnant creature. I interpreted that scene that the ring hated Bilbo because he gave him up.
Frodo needed to use the ring to escape from Boromir and while he thinks that he coincidentally climbed up the seat I think the ring influenced him to have an opportunity to reveal himself to its master. It was only one moment where Frodo was able to resist and defeat the attempt of the ring.
Boromir
The ring sensed that Boromir was desperate to save Gondor and I think that during the long voyage it seduced and tortured him by invoking feelings of omnipotence.
Finally he requested to see the ring during the breakup at Amon Hen before attacking Frodo.
