It has been stated by many that correct Arabic pronunciation would be 'Raas.'
The correct Arabic pronounciation is Ra-us, though Ras is close enough. wiki
This is this bit from Batman Beyond in which Terry says "Raas" and is subsequently corrected by Talia to say "Raysh." This made it a sore spot for me when new Batman trilogy decided to use "Raas."
There are several unsubstantiated (or cited) claims that the creator used and intended 'Raysh.' Indicating a preference for the Hebrew pronunciation for the word.
The correct [Arabic] way is closer to 'rahs', the way Denny O'Neil (the writer who created the character) intended it to be said is 'raysh'. The the DCAU went with 'raysh', the Nolan movies went with 'rahs'. reddit
On the embedded video there is also a dubios comment which states:
The creator of the character meant for the pronunciation to be the Hebrew pronunciation Raysh, probably because of the whole Lazarus [pit].
Then there is this quote from Executive Producer Marc Guggenheim from Arrow.
One key issue I wanted to bring up, because it came up last season when I wrote about that third episode, is the pronunciation of Ra's al Ghul's first name, which has traditionally been something close to "Ras" or "Ross" when referred to colloquially, but becomes something closer to "Resh" or "Reesh" when savvy fans discuss him.
"The beauty part of what you guys do is you just have to type it and it's the same spelling even if it's a different pronunciation," Guggenheim laughed. "Basically what we decided to do, and I think you sort saw this in Episode 2.13 when Nissa came to town, is we basically honored the two different pronunciations, some of our characters saying 'Ras' and the ones sorta more in-the-know say 'Resh' and that struck us as a very reasonable compromise. There are clearly two different schools of thought and we wanted both to be represented."
So he seems to think 'Resh' (or 'Raysh') is the more correct pronunciation for the name.
At a recent San Diego Comic Con panel there was some discussion about "Raz" versus "Rayche" from David Ramsey and Stephen Amell.
He explained why some characters pronounce "Ra's" "Raz" while others say "Rayche." "If you are part of the League of Assassins, you say 'Rayche.' It's a sign of respect and the proper way to pronounce it. If you are outside the League and you're rogue, as a sign of disrespect, you say 'Raz.'" That understanding came about because the actual pronunciation was not clarified on the set until episodes with the "Raz" pronunciation had aired, so, "we had to create a mythology."
At least for Arrow, "Raysh" (or "Rayche") is the correct pronunciation, while "Raas" (or "Raz") is a more derogatory version. In the DCAU, "Raysh" is also the correct version.
For the cinematic Dark Knight trilogy, the correct pronunciation is "Raas."