Sean Astin did not receive an Oscar nomination for portraying Samwise "Sam" Gamgee in The Lord of the Rings: The Return of the King.
Sean Astin portrays Frodo's fellow Hobbit and best friend who has been with him along his whole long journey to destroying the ring. In the other two films Astin offered fine support as Sam who always act loyal to Frodo being the only member of the original fellowship to go with him to actually attempt to destroy the ring. Astin is good in both he previous films, and does have some very nice moments but it is not until this film where he really gets to fully shine in the part of Samwise.
In the role throughout all of the films but especially this one, where one could argue that Sam becomes the true hero of the entire film, is the perpetual optimism of Sam. Astin portrays this particularly well because unlike say the Ralph Bakshi where Sam just comes off as stupid, Astin shows it as something entirely genuine within Sam to simply try to see the brighter side of things even in the darkest of situation. Astin does overplay it any way only portraying Sam's strong beliefs in good triumphing over evil in a honest fashion that is perfect for Sam.
What is perhaps the most important aspect of Sam in the series is his friendship with Frodo. Astin and Wood depict it in a very quiet and understated fashion that work wonderfully well. Importantly though Astin shows his love for his friend as something that endures all the pains of the adventure, and that is really what keeps him still trying his best to remain positive even as Frodo becomes slowly more and more depressed over their hardships. Astin makes their key moments together quite moving though because he just is so truthful in finding the unending passion within Sam to help his friend.
Sam being the first film as rather afraid and unsure of himself so much that he hesitates to leave his home. In this film he goes all the way to taking on a giant spider all by himself. That is certainly not an easy transition to make believable, but Astin does just that. It is a well handled transition slowly through the film, but it is not that Sam necessarily becomes a different person, Astin certainly does not play it that way nor should he. Astin rather more effectively portrays a bravery that simply was always in Sam, and simply the situations is what broke him out of the hesitations he had beforehand.
One thing that certainly works in favor of the films is the down to earth performances given by much of the cast despite the fact that it is a fantasy film. This is especially true of Astin whose reactions to the situations he goes through, as well as his slow physical and mental trauma from the events, as the reactions of any man, not even necessarily a hobbit. Astin just has the utmost conviction in his part to make every moment especially the most poignant ones, such as "I can carry you", come through with the power they need for the film. This is a strong performance from Astin that finds just the right tone for his character, and powerfully carries it through the film.