This only will be about the original "Arthur Adventures" book series not the spin-off books like the "Step-into-Reading" ones, the D.W. ones, the chapter ones or the later sticker ones, stuff like that (like D.W.'s Guide to Perfect Manners.)
It is interesting how there are still some Arthur books that were not adapted into episodes of the TV series, along with some that were heavily modified when adapted, and some books adapted from the TV series as well. Here is a list of the "Arthur Adventures" book series and their adaptation status...
1. ARTHUR'S NOSE (1976) - Will obviously not be adapted as it would not fit within the context of the series; Arthur's original long aardvark-esque nose shrunk as a result of art evolution (though I remember on the PBS website there was an Arthur fan story a kid submitted featuring how their noses got shorter!) The only other recurring characters appearing are Arthur's parents and D.W. (she was not named yet by this time, only referred to as "Arthur's sister") and Francine (looking more monkey-like, complete with tail!) Arthur and Francine are also in the first grade in this story.
2. ARTHUR'S EYES (1979) - Already adapted as Episode 1A, and a pretty faithful adaptation as well (the book version even had the infamous girls' room sequence!) This book also introduced Buster, Mr. Elkin (or Mr. Marco as a moose) and Mr. Haney (unnamed.) Instead of Arthur seeing Wilbur Rabbit wearing the same glasses on TV, he feels better when he sees Mr. Elkin's reading glasses looking just like his. The cover artwork was redone around 1996-1997 featuring Arthur's newer design.
3. ARTHUR'S VALENTINE (1980) - Has not been adapted yet as of 2012. This one introduced Fern and Sue Ellen, as well as the whole Arthur/Francine hinted romance. Valentine's Day was mentioned in "The Long Dull Winter," but never had an episode focused on the holiday. Arthur can also be seen with a Bionic Bunny lunchbox, marking the debut of said character.
4. (ARTHUR AND) THE TRUE FRANCINE (1981) - Was adapted both into an episode of the same name (Episode 14B) and partly into "Arthur and the Real Mr. Ratburn" (Episode 2A.) The book version had them starting third grade, and introduced Muffy Crosswire and Mr. Ratburn. The TV version of "Arthur and the True Francine" was told as a flashback when Muffy joined up in their second grade class as a new student in Mr. Marco's class.
5. ARTHUR GOES TO CAMP (1982) - Was adapted into Episode 7A. The book version introduced Alan "The Brain" Powers. Additionally, the boys had a tough male counselor named Rocky while the girls got Becky; the TV version only had both genders getting Becky. Again, a rather faithful adaptation.
6. ARTHUR'S HALLOWEEN (1982) - Has not been adapted yet as of 2012, and probably won't be, as they already did two Halloween-themed episodes, "The Fright Stuff" and "Hic-or-Treat." The book apparently flashes back to when Arthur was in second grade, and also marks the debut of Mrs. Tibble (depicted as a human in all of the non Step-Into-Reading books), as well as D.W. getting named ("D.W. must be short for Dim-Wit," Arthur comments.)
7. ARTHUR'S APRIL FOOL (1983) Has not been adapted yet as of 2013, and the chances of it getting adapted are slim as it might not fit into the current continuity unless told as a flashback. Needless to say, the book introduced Binky Barnes, but back then he was just a school bully who threatened to pulverize Arthur, and was not mentioned as being held back in Mr. Ratburn's class (the book does have Arthur and his friends in third grade.)
8. ARTHUR'S THANKSGIVING (1983) Has not been adapted yet as of 2012, and probably won't be, as they already did a Thanksgiving-themed episode, "Francine's Pilfered Paper." It has Arthur directing Mr. Ratburn's Thanksgiving play, and also marks the debut of Muffy's catchphrase "Vomitrocious!"
9. ARTHUR'S CHRISTMAS (1984) Has not been adapted yet as of 2012, and probably won't be, as they already had "Arthur's Perfect Christmas." This one takes place when Arthur is in second grade, and he decides to find a perfect gift to give Santa Claus. It also marks the debut appearances of Grandma Thora (unnamed by this point) and her dog Killer (who did not appear in the animated series until the ninth season.) Worth of note, Francine also sits on Santa's lap in the book, as this was before the TV series came around and established her family as Jewish.
10. ARTHUR'S TOOTH (1985) Was adapted into Episode 24A. In the book version, it flashes back to Arthur being seven and still in second grade. Not much was changed aside from the second grade difference, though Francine doesn't sneeze her tooth out, the film they watch is on an old 16mm projector instead of a VHS tape, and isn't a Power Rangers parody. The shark tooth bit was also added for the TV version, along with the Brain's tooth-removing machine having a self-destruct mechanism, along with Francine's tooth fairy game involving a soccer ball (in the original book, Francine says "Whoever I touch loses a tooth! The one who loses the most teeth wins.")
11. ARTHUR'S TEACHER TROUBLE (1986) Was adapted into Episodes 2A and 2B, "Arthur and the Real Mr. Ratburn" and "Arthur's Spelling Trubble," respectively. In fact, home video releases retitled Episode 2A as "Arthur's Teacher Trouble" to coincide with the book. This book also apparently clashes with the continuity of the book version of "The True Francine." The spelling test is also a traditional written test in the book version instead of a classroom spelling bee. I believe the book version also introduced Prunella, and also began to feature the more current character designs.
This book was also adapted in early 1993 into an award-winning interactive animated storybook PC game from Living Books (now Wanderful Interactive Storybooks) and is also currently available for iOS devices.
12. ARTHUR'S BABY (1987) Was adapted into Episode 11A. The book version is not a flashback, and introduced Baby Kate into the Arthur universe. Otherwise, it's a pretty faithful adaptation (even little bits, like Arthur's "Is it a new bicycle?" and Buster's warning about more than one baby are carried over to the TV version.)
13. ARTHUR'S BIRTHDAY (1989) Was adapted into Episode 10A. I think the TV version has them in second grade, seeing as it was Arthur and Muffy's eighth birthdays in May. Still a pretty faithful adaptation, though the party store scene takes place before Arthur is aware of Muffy's party, and the tug-of-war game and the pinata that won't open is exclusive to the TV version. Exclusive to the book version is a bit when Arthur gets a birthday card from Uncle Bud (who appeared in Episode 11B, "Arthur's Cousin Catastrophe.") Again, this was adapted in 1994 into another Living Books/Wanderful Interactive Storybooks game that is also currenty available for iOS.
14. ARTHUR'S PET BUSINESS (1990) Was adapted into Episode 5A. This introduces Pal into the Arthur universe, along with Mrs. Wood and Perky. Again, a faithful adaptation for the most part. The Amazing Larry from this book also appeared in Episode 18B, "Sick as a Dog," but as a rabbit-like character instead of a human as in the book.
15. ARTHUR MEETS THE PRESIDENT (1991) Has not been adapted yet as of 2012, and probably will not be, as Arthur had already been to Washington D.C. with his family in "D.W. Goes to Washington," but the book has him going with his whole class as they had won a contest. The president is also a more generic one in the book instead of the Bill Clinton-esque aardvark in "D.W. Goes to Washington." The book version also first gave Mr. Haney his name (as he was originally just referred to as "the principal" in prior books.) It's possible it could be adapted and modified due to the changing of presidents over time, but it's still unlikely.
16. ARTHUR BABYSITS (1992) Was adapted into Episode 9A. This book introduced the Tibble Twins, both of whom were human boys wearing cowboy hats, and continue to be humans in non-Step into Reading Arthur books by Marc Brown. The Sugar Bowl is also introduced in the Arthur universe, and Arthur babysits the Tibbles in the evening in the book version instead of in the afternoon. Otherwise, a rather faithful adaptation.
17. ARTHUR'S FAMILY VACATION (1993) Was adapted into Episode 15A. A pretty faithful adaptation, though exclusive to the book version is the last day of school being depicted, and a visit to an alligator zoo called Gatorville between the cow festival and Flo's Fudge Factory scenes. In the UK, the book is called "Arthur's Family Holiday," and more recent re-prints recolored Sharky from its original orange to a more bluish color (possibly to reflect Sharky being purple in the TV series.)
18. ARTHUR'S NEW PUPPY (1993) Was adapted into Episode 8A. Pal is named in the book version, and is a somewhat faithful adaptation.
19. ARTHUR'S CHICKEN POX (1994) Was adapted into Episode 18A. D.W.'s full name is also revealed in the books ("Dora Winifred, I'm very disappointed in you!") Again a rather faithful adaptation, except Arthur does not hallucinate a large blue elephant when in school, and D.W. is more concerned about missing the circus at the end of the book version instead of being happy she caught the chicken pox.
20. ARTHUR'S FIRST SLEEPOVER (1994) Was adapted into Episode 30A. Bitzi Baxter makers her debut in the book. Exclusive to the book version is that when Dad reads about the man claiming he saw a spaceship, Mom jokes "Probably the same man who thought he saw Elvis at the mall," along with the tent being a lot bigger, the boys making signs to welcome aliens and getting a pizza delivery during the sleepover, and when D.W. fakes a spaceship with the flashlight, the boys run around detaching the tent over their heads and crashing into a tree, instead of the tent just collapsing on them. Exclusive to the TV version are the three boys' dream sequences (including Arthur's hilarious nightmare about D.W. wanting to come to the sleepover) and their impromptu model spaceship.
21. ARTHUR'S TV TROUBLE (1995) Has not been adapted yet as of 2012, and might not be, as a similar "working up to buy the product" device was also used in Episode 8B, "Arthur Bounces Back." The book version introduces Mr. Sipple, and Sue Ellen's current design. The plot is about Arthur seeing a commercial for a "Treat Timer" dog treat contraption that he wants to buy for Pal, so he works up to save enough money to buy it, only to learn a lesson about things not always being as advertised on TV.
22. ARTHUR WRITES A STORY (1996) Was written/published at the same time as the TV version, Episode 12A, was, and credited as "Adapted from a teleplay by Joe Fallon."
23. ARTHUR'S COMPUTER DISASTER (1997) An adaptation of Episode 14A, "Arthur the Wrecker" (retitled for home video as "Arthur's Computer Adventure.") It was adapted into a Living Books game in 1997 as well. (With that said, I think a better title for the episode version should have just been "The Game.")
24. ARTHUR LOST AND FOUND (199 An adaptation of Episode 39A, "Lost!" except Buster joins Arthur on the bus.
25. ARTHUR'S UNDERWEAR (1999) An adaptation of Episode 35A. The UK version is titled as "Arthur's Pants."
26. ARTHUR'S TEACHER MOVES IN (2000) An adaptation of Episode 70B, "The Rat Who Came To Dinner."
27. ARTHUR TURNS GREEN (2011) Has not been adapted yet as of 2012, but there is a chance it could be adapted in the future, as it's a more recent book, and the first new one in the Arthur Adventures series in eleven years.
Also worth of note is a 1984 book "The Bionic Bunny Show." This book was not in any of the Arthur series books, but takes place in the same universe, and also introduces the character Wilbur Rabbit, along with a proper introduction to the Bionic Bunny character and franchise. A few things from this were carried over to the TV episodes "Arthur's Eyes" and "Arthur Goes Crosswire."