It depends on you and your child.  I took my five year old daughter to it and she was not scared and we discussed the underlying truths of the movie during it as well as after the movie.  Namely that the young boy was having a lot of feelings about his parents divorce, had a lot of anger and wasn't feeling heard or seen.  In the world he created he was trying to take care of everyone but he began to realize that no one can really do that.  It's not possible to make everyone else happy and "fix" a family and through his imagination the boy was able to move through his feelings of loss and sadness that were coming out as anger.  If your child just wants to go and see a funny ha-ha silly movie this may not be for them, although there were funny parts in it.  But if you want your child to understand more about life and reality and feelings that it's a great opportunity to be real with kids about real situations they may face. Children are much more complicated and diverse than we often think they are or give them credit for.

It is completely unsuitable for young children, for two reasons. First, it is really scary. The "wild things" are beautifully imagined and constructed, but they do terrifying things that wouldn't make sense to a child, and Max appears to be in danger--a young child wouldn't get that this is a fantasy or a parable. (Of course this will depend on the child--a five year old who is used to seeing a lot of violent action movies--e.g., Batman--won't be any more troubled by this than what he or she has seen already. But a very tender-hearted ten year old could be quite unnerved.)
 
Ten-year-olds who aren't easily rattled would probably be fine, and might really profit from a conversation about how the movie is a metaphor for what goes wrong when people are locked into particular ways of responding to sadness or anger.
 
However,  the difficulties that the wild things have in getting along are very adult; they remind me of people my age trying to live in a collective--their characters are completely recognizable, as you'll see if you see it. Go with a bunch of over-50s, not under 10s!

I haven't seen the movie yet, so I posted this question to my Facebook profile to see what my parent friends who had seen the movie would say.
 
Here are two comments received....
 
From a mom of a 9 year old and 5 year old:
"It's dark but very beautifully done. I did have to explain a bit about Carol (one of the wild things)'s behavior to my kids who were a little confused I think by him ....but happy ending and got them thinking!"
 
From an elementary after-school program and recess yard helper (with two grown children):
"Many of the kids at my school have seen it & thought it was very cool. They like all that scary stuff & so did my kids."
 
As for me:
I'm thinking I'll go see the movie myself without our daughter (who can be a bit sensitive to scary or dark-themed movies), to see if I think it's ok for her to see. That could be a solution for you too.

I would not bring young children to this movie. I found this movie dark and sad, its themes are complex- I was surprised by how adult it was considering the book and the advertising. Max is in danger of being eaten at several points, someone looses an arm. I'd definitely preview first if you are planning on bringing children to it.