Why didn't Frodo just give the ring to Gollum?

[The Dark Elf]

It would've been a lot easier on frodo and his friends and all of their friends if he gave the ring to Gollum. Gollum would hide in a cave and constantly be on the move, but Sauron wouldnt care about Frodo or Gondor or anything but Gollum.

[Knight of Gondor]

Dark Elf...please don't take insult in this...but that's kind of a moot -- silly? -- question. Of course Frodo wouldn't want to give the Ring to Gollum, his ultimate aim was to destroy the Ring! Perhaps if he were only concerned for his own selfish fate, then he might give the Ring to Gollum or someone else to jump ship and save himself. But that wasn't who he was.

Plus, he took pity on Gollum, and to give it back to him would be like turning a druggie you're trying to reform right back over to his drugs.

[Lord of Angmar]

Because it would have ensured a victory by Sauron.

Sauron would have vanquished his enemies if the Ring had not come into play at all. The 'good guys' only won the day because of the destruction of the Ring. Also, Gollum would have an equal - if not greater - chance of being caught by servants of Sauron.