I already loved these guys in Attack of the Clones as they had several classic moments together but in Revenge of the Sith they really outdo themselves in terms of humor and swagger !
A list of my favorite moments between the two of them, and forgive me for the inevitable misquotes. I've only seen the movie 3 times so far.
-Anakin smiling and saying "this is where the fun begins."
-Anakin wanting to go back and help the other pilots while Obi-Wan reigns him in about how they are doing their job so the Jedi can do theirs.
-Anakin refusing to go on without Obi-Wan when his friend gets covered in buzz droids.
-Anakin shooting off Kenobi's wing and then saying "I agree, bad idea."
-Obi-Wan screaming at Anakin, "have you noticed the shield is still up ?!?"
-Obi-Wan telling Anakin that they are walking into a trap, Anakin asking what the next move is, and Obi-Wan answering with a smile "spring the trap."
-Obi-Wan asking Anakin if he stopped the elevator and Anakin replying by asking if Obi-Wan did it.
-Anakin cutting a hole in the elevator ceiling, jumping through it, and Obi-Wan cracking "always on the move."
-Obi-Wan starting to explain the gaffe as being Artoo's fault when Anakin cuts him off in defense saying "ahh ah, no loose wire jokes." and then later adding that Artoo is trying.
-Obi-Wan telling Anakin that they will take Dooku together this time and Anakin replying "I was going to say that."
-In reply to Grievous busting Ani's balls about his youth, he says "General Grievous, you're shorter than I expected." and Obi-Wan piling on with "Anakin we have a job to do, try not to upset him."
-Anakin saying Obi-Wan's fate will be "the same as ours" when Palpatine wants to leave Kenobi for dead.
-Obi-Wan waking up in the elevator shaft on Anakin's back, then Anakin telling him "we're in a situation here."
-Obi-Wan telling Anakin "we still have half a ship" while Anakin is trying to save the landing.
-the entire "Poster Boy" scene after they arrive at the Senate via airbus, that whole exchange was awesome and the comments back and forth were great. Anakin saving Obi's skin for the 10th time but then being corrected that it was only the 9th because that business on Cato Neimodia didn't count.
-The discussion between them after the Council accepts Ani's suspicious appointment to the Council. I really felt for Kenobi and how torn he was, saying he was on Anakin's side and didn't want him to get involved. Then clarifying that "The Council" was asking that of Anakin and not Obi-Wan himself.
-Their last friendly discussion as Obers leaves for Utapau. Anakin's apology and Obi-Wan's speech is so reminding of Obi's apology and Qui-Gonn's speech in TPM. The goodbyes and "May the Force Be With You" were very touching.
-After Anakin becomes Darth Vader there is some great stuff between them before and after the duel. As Kenobi stands on the ramp of Padme's ship, Anakin's "you will not take her from meeeeeeeee" was so creepy and chilling. Kenobi chatting things up a bit but then saying, resolved, "I will do what I must" and Anakin's reply of "you will try" ooooooh did that ever get me as well. Also, the talk about the Republic vs. the Empire was outstanding.
-Obi-Wan telling Vader that he has the high ground, it's over, don't even try it, because obviously Obi-Wan knows that Ani/Vader is going to go for it anyway and that's how he takes him out.
-The entire "You were the chosen one" segment, was that ever incredible. Chilling, just chilling for me. "I loved you like a brother." Powerful stuff.
That's all I can come up with for now, but I'm seeing the new Star Wars again on Saturday and Sunday so I will add whatever I missed / forgot later.
I said they are now my favorite onscreen duo of all time, so just for reference I will say that some of my other favorites are
-Han Solo and Luke Skywalker from Star Wars 4 thru 6
-Peter and Roger from Dawn of the Dead (1978)
-The Dude and Walter Sobchak from The Big Lebowski