I've just started reading Fellowship of the Ring so I'll type the film characters then come back when I've finished later and give my take on the book versions
Froddo- ESTP he pranks Gandallf in the beginning as he arrives, also when he had the ring he shouted a lot
Sam Gamjee- INTJ very easy one
Peregrin "Pippen" Took- ISTP strong second-breakfast vibes
Mery- INFP
Billbo- ENFJ he talks to the entire crowd at his 111th birthday party
Gandelf- ESFJ talks to Frodo a lot about his past adventures with Bilbbo so Si, knows all the different creatures and races over middle earth so Fe, I was drawn to ISFJ but I think he leads with his Fe
Aragone- ESFP always in the moment, good in a fight, F because he loves Awren
Gimlie- too hard to type, he doesn't have enough talking moments in the films, but I'm pretty sure xNxx
Legalas- ENTP or ESTJ, I'm leaning more to ENTP because his high Ne, like the scene where he shield surfs in two towers showing his capability to use things in non traditional ways
Boramir- INFJ he worries a lot about Gondor and says "Gondor needs no king" Ni. Played by Sean Bean so clearly an FJ
Elrrond- ESTJ
Arwin- ENTJ daughter of Ellrond so would naturally have some authority, and when the Nazgul are chasing her she swears
Saruman- ISFP places his values on things a lot, is very practical and realistic, like when he tells Ganndalf we must join Saron, and says to Aragon that he will never be crowned king in the extended edition
Andy Serkis' character (I can't remember it's name sorry)- ISTJ
King Thoeden- ENFP definitely an extrovert and he cries in the scene after his son's funeral
Eomer- ISFP "I would cut off your head dwarf if it stood but a little higher from the ground" Se, the first thing he pays attention to is Gimley's size so he focuses on details
Eowin- ESTP wants to go out and fight but can't because she's a woman
Galadrel- ESTJ and very much so, in the scene where Fredo tries to give her the ring she goes crazy and mad then swore at him
Denathor- ISFJ obsessed with his power and picks a favourite son
Faremire- ISTP very similar to Pippan which is why they bond so well
Grima Wormtongue- ESFP knows how to manipulate Theodin and gets around from Rohan to Isengard well so probably an extrovert