I have ridden at a barn that raises and trains Arabs for show. The barn also gives lessons on some of the more experienced horses, all of which are arabs except for one lovely Appy (in fact, she's the only horse at the barn that isn't at least part Arab). Anyway, I have worked with many, many Arabs, from endurance/trail types to $60,000 national champs.
As people have said, it varies so much on the individual horse. I'm currently riding a 4-year-old arab that is a complete sweetheart and rides like a dream! He has personality and spunk, but I also feel very safe and in control while riding him. On the other hand, I also leased a 5-year-old Arab that was completely unpredictable (but still a joy to ride). And I would trust many of our lesson horses with pretty much any rider.
I love Arabs completely, and encourage you to get one! They are beautiful and very fun to ride and interact with. I only encourage you to get to know the individual pretty well before you buy. I have found that they can be a bit difficult at times, and if they don't like you, they aren't afraid to let you know. :) Find one that you connect with!