His job was to destroy the ring. Nobody would just send him there, they told him to throw the ring in the vulcano.

: Moreover: I don't think he failed at all. Don't you find it strange, that when Gollum attacked him at the Cracks of Doom, he so easily overcame Frodo and bit off his finger? Only a few minutes before that, when Gollum attacked him for the first time, it says that "Frodo flung [Gollum] off and rose up..."
: I don't know about you, but I see an obvious paradox here: if Frodo was able to overcome Gollum even before he claimed the Ring (which was supposed to increase his power), then how come he wasn't able to overcome Gollum while wearing the Ring? Isn't it more logical to assume that Frodo *let* Gollum bite his finger off, and then *commanded* him to fall into the fire, after warning him twice:
: "If I, wearing [the Ring], were to command you, you would obey, even if it were to leap from a precipice or to cast yourself into the fire. And such would be my command". [The Two Towers, Chapter"The Black Gate is Closed"]
: and:
: "If you touch me ever again, you shall be cast yourself into the Fire of Doom". [The Return of th King, chapter "Mount Doom"].

Those two statements were said to threaten Gollum, Gollum was no ringwraith, so the wielder of the ring had no power over him. It was the ring itself or rather the urge for the ring that controled Gollum.
When Frodo flung Gollum off, he used the last of his own power. At the cracks, the ring had complete control over Frodo, but Frodo was physically worn out and could not withstand Gollums furious attack. If Frodo had the power to make Gollum fall and destroy the ring, he certainly had the power to destroy it himself.
Besides, Gollum danced around a bit with the ring before he fell, and then Frodo had no power over the ring and thus no power over Gollum, so he could not have commanded him to fall.

: So I think that despite the fact that Frodo was tempted to claim the Ring, he later overcame his temptation, and willingly destroyed it, using Gollum.
: And that means he did *not* fail: he destroyed the Ring.

In this story he failed, but if Gollum wasn't there maybe he would have come to his senses again (probably with a little help from Sam) and might have completed his task.

: Now you can flame me as much as you wish.

You, you Frodo!! ;-)

Maglor