[Boromir88]

I think there are several determining factors when it comes to one's resistance/temptation towards the Ring. I also think there is a level of importance as far as how easily one is tempted. In my opinion, these are the order of important factors when it comes to one's fall/corruptability of the Ring. And this is sort of just my personal feeling, and can easily be debated.

1) The circumstances one acquires the Ring
2) The mindset/personality of the individual
3) The knowledge of the Ring
4) The Time of Possession

I'll first start out with the fact that I don't think how close one gets to the Ring, or any 'physical contact' with the Ring effects the person's corruptability. You bring up Boromir who only sees the Ring, and never really touches it. I'll further explain Denethor, but just to point out, Denethor never comes even close to seeing or touching the Ring, yet he shows a desire to possess it, and it is because he falls into the factors above.

1) The circumstances one acquires it-

Gandalf makes clear that if one is 'good intended' when they acquire the Ring, the corruption of them is slower:

"Yes, sooner or later - later, if he is strong or well-meaning to begin with, but neither strength nor good purpose will last - sooner or later the dark power will devour him."~Shadow of the Past

If one acquires the Ring under 'good intentions' the corruptability is a lot slower. Bilbo is one who does this:

"Pity? It was Pity that stayed his hand. Pity, and Mercy; not to strike without need. And he has been well rewarded, Frodo. Be sure that he took so little hurt from the evil, and escaped in the end, because he began his ownership of the Ring so. With Pity."~ibid

Counter that with Gollum, who murders to get the Ring, and his fall and the strong hold of the Ring over Gollum happens a lot sooner than it would Bilbo. (Bilbo after 60 years was still in an 'early stage' of influence towards the Ring, because of the circumstances where he got it and the other factors).

2) The mindset of the individual-

Are they someone who desires power and glory for themselves? Like Boromir? Or someone who is much more simple and knows what they have is good enough for them, like Sam.

Boromir is in the mindset that the Ring is a weapon for him, and it will give him power to command, this makes him an extremely easy target for the Ring:

"What could not a warrior do in this hour, a great leader? What could not Aragorn do? Or if he refuses, why not Boromir? The Ring would give me power of Command. How I would drive the hosts of Mordor, and all men would flock to my banners."~Breaking of the Fellowship

So, it is Boromir's personality and his refusal to accept the Council's words that using the Ring against Sauron would bring everyone's downfall. To put it as Faramir would say, he could see exactly why Boromir would be allured to it, because to Boromir it would be seen as a weapon and he would be glorified.

We see this very thing in Denethor, who never even comes close to the Ring, where at least Boromir is with it. But, it is Denethor's prideful personality, and his thought of "I would do anything to save my Realm" that makes him susceptible to the Ring:

'He would have brought me a mighty gift.'
[...]
'Nay, it should be kept, hidden, hidden dark and deep. Not used, I say, unless at the uttermost end of need...'
[...]
'If I had this thing now in the deep vaults of the Citadel...'~The Siege of Gondor.

Denethor already desires to possess it, and eventhough he says it should not be used, he shows a want to possess it. And he puts conditions upon the Ring...'I won't use it unless I absolutely have to.'

And as the antithesis of Boromir and Denethor, is Sam. Who actually does possess the Ring, and hold it, though for a short while. However it's Sam's mindset that is able to make him give the Ring back:

In that hour of trial it was the love of his master that helped most to hold him firm; but also deep down in him lived still unconquered his plain hobbit-sense: he knew in the core of his heart that he was not large enough to bear such a burden, even if such visions were not a mere cheat to betray him. The one small garden of a free gardener was all his need and due, not a garden swollen to a realm; his own hands to use, not the hands of others to command.~The Tower of Cirith Ungol

Sam knew the Ring was trying to treat him, but he was a simple hobbit, and the temptation of turning the Gorgoroth into a grand and beautiful garden, he rejected, because his 'small garden' was good enough for him.

3) Knowledge-

Bilbo didn't know much about the Ring, and he saw it as an occasional trick and fun play:

..."How long have you known this?" asked Frodo at length. "And how much did Bilbo know?"
"Bilbo knew no more than he told you, I am sure," said Gandalf. "He would certainly never have passed onto you anything that he thought would be a danger, even though I promised to look after you. He thought that the ring was very beautiful, and very useful at need; and if anything was wrong or queer, it was himself. He said that it was "growing on his mind," and he was always worrying about it; but he did not suspect that the ring itself was to blame. Though he had bound that the thing needed looking after; it did not seem always of the same size or weight; it shrank or expanded in an odd way, and might suddenly slip off a finger where it had been tight."~Shadow of the Past

Gandalf certainly knew more about the Ring than Bilbo, and this would make him far more dangerous as a possessor, knowning more about the Ring and it's maker.

4) Time of Possession-

As Gandalf puts it, no matter the circumstances one gets it, good-intentions or not, the Ring over time the Ring will eventually gain control over the bearer. But, I don't think it's as big as a factor as the other ones seem to be, as it appears that if you have a simple mindset like Sam, or good intentions, you could resist the Ring.

I hope that answers it. Boromir fell to the Ring, because of his personality and it made him a target for the Ring even before he knew or came across it. The Ring preys on individuals like that. And had Denethor come across the Ring, he too would have tried to take it, because of his mindset.