The Lord of the Rings ended with triumph. Sauron's One Ring was destroyed, and the Dark Lord's efforts were thwarted. Because of that, Aragorn was crowned king of Gondor, and his reign ushered in an era of unprecedented peace. However, the free peoples' ultimate triumph shouldn't overshadow the tragedies that countless people endured. Sauron's bid for power resulted in hardship and suffering in Middle-earth. Even Frodo had to travel to Valinor to be healed of his spiritual wounds.
Sauron's bid for power didn't hurt anyone more than Gollum. Originally, Gollum was a Stoor Hobbit named Sméagol, but having the Ring for 500 years twisted him beyond recognition. After he lost it, Gollum was distraught and did his best to regain his Precious, which he did in the final seconds of his life. He bit the One Ring off Frodo's finger before being "pushed" to a fiery death. It was a tragic end, but it's worth noting that J.R.R. Tolkien actually blamed Sam for Gollum's death.
Gollum Could Have Been Redeemed
The first time that Gollum appeared in The Lord of the Rings was in Fellowship of the Ring. The Fellowship was traveling through Moria when Frodo spotted him in the distance. Frodo wasn't pleased that he was following them, but Gandalf told Frodo that Gollum deserved pity. Flash-forward to The Two Towers, and that's what Frodo gave him. He gave the pitiable creature a chance at true redemption -- and Gollum was starting to take it.
Gollum and Sméagol were competing personalities, but thanks to Frodo's encouragement, Sméagol was winning out. He had sworn allegiance to Frodo, and he did exactly what he had promised. He took Frodo to the Black Gate, and he found an alternate route into Mordor. He even saved Frodo during the Dead Marshes scene. All of that indicates that Sméagol was fighting the influence of the One Ring. Unfortunately, Sam wasn't convinced by Gollum's redemption.
Why Sam Was Responsible for Gollum's Failed Redemption
While Frodo was trying to help Sméagol, Sam wasn't having any of it. He constantly berated Sméagol for anything and everything, and according to Tolkien, that was why Gollum was never redeemed. There was a moment in The Two Towers book where Frodo and Sam were napping on the Stairs of Cirith Ungol when Gollum came up to them. After a moment of inner turmoil, it looked like Sméagol had finally won out. He even caressed Frodo's leg before Sam awoke and accused him of "sneaking."
According to Tolkien, that exchange was one of the most tragic parts of the Lord of the Rings story. In Letter 246, he explained that "Sam fail[ed] to note the complete change in Gollum's tone and aspect. 'Nothing, nothing', said Gollum softly. 'Nice master!'." Thus, it was only seconds after his near-redemption that Sam was back to accusing him of foul play. Tolkien went on to explain how Gollum's repentance was ruined by Sam's brash and defensive comments.
Of course, Sam had to act that way for The Lord of the Rings' narrative, so he can't really be blamed. But still, if Sam hadn't acted in such a way, Gollum could have been redeemed. Tolkien even hypothesized an alternate ending where Gollum took the Ring from Frodo so that he could willingly sacrifice himself and save his master. In that way, Sam was responsible for Gollum's death -- because he prevented Gollum from being redeemed.