The Bakurae sections are the most heavily changed from manga to anime.

Starting with Duelist Kingdom, first he obvious: Because Monster World was done in series one, they had to do a translation of it to fit into Duelist Kingdom, so right off the back, back-story and such is utterly changed. They make it seem like Bakura didn't know Yuugi-tachi at all beyond knowing them from school. (I mean, they changed Bakura's transferring in section completely: Flashback cap #1 & Flashback cap #2 compared to: the manga version No wonder he looks so depressed in the anime version. ><)

Then you have the cutting out of Yami Bakura resurfacing from the Maze section, as well as cutting out most of Bakura's actual screen time [He's reduced to dueling commentary, nothing about him wanting to find out about the Sennen Items, nothing of him reflecting on Kaiba being in a similar situation as Yuugi, hell, none of him wanting to help Honda look for Mokuba (just him saying that Honda's insane for crawling around and up the castle in the middle of the night looking for how Pegs is cheating] or him being even part of the gang proper. He doesn't even get to be part of the protecting Yami Yuugi from the Mind Scan squad because of the next changes:

First, you have the change of when Yami Bakura wakes up from when he makes the deal with Bakura that if he puts the Ring back on, he'll help Yuugi-tachi escape from the maze because Yami Yuugi always waits for the last second to do anything. Bakura never took off the Ring after ep 13 in the anime, where as manga wise, he just had the Ring with him and didn't wear it because it was dangerous [Personaly, if something I wore had or had had a spirit in it that took over my body, I wouldn't wear that bugger again no matter how spiffing it looked or who gave it to me.] It's translated over to Yami Bakura waking up when the non-dueling trio gets sucked through the tower floor turned to grape jelly to the basement Yami no Game room. In the manga, that night Honda went out by himself to try and find Mokuba and Bakura bumped into him after his yami had taken the body for a joy ride to snigger at Shaadi's portrait [*side rant here about how Shaadi's character/appearances/ect are the most changed of all*] Bakura distracted the guards while Honda sneaked into the basement and after Honda was captured, Yami Bakura rescued him and the next you see Honda and Bakura, Honda's carrying Mokuba as Jounouchi rushes past looking for the card Bandit Keith stole, and Honda and Bakura show up at the dueling stage for Yami Yuugi vs Pegasus. 

The change that Yami Bakura wanted to hunt after Mokuba for the key to Kaiba corp. makes no sense. The dub changing to him wanting Mokuba's soulless body makes much more sense, sadly. What the heck would he want with the key to Kaiba corp.? Doesn't help him get the items at all.

The Yami Bakura vs Pegasus part you don't see happen in the manga, you just see Pegs missing the eye, Yami Bakura leaving him the replica [that Bakura asked Yuugi if he could have from the eyeball soup] and cackling as he walks away.

Other general changes is Duelist Kingdom: Bakura doesn't have a deck, Yami Bakura doesn't make cards come to life, Honda doesn't throw away the Ring [no one's aware that Bakura's wearing it again]
 

Next section: DDM and Battle City. Yes, Bakura was there for both in the manga! :)