I've found where I can set that an entire forum have all posts sent into a moderation queue (thanks Ruben) but what I really want is to have posts from only certain users sent to this moderation queue.

For instance: all users can post to the Suggestions Forum except posters A, B, and C.

To accomplish this, I tried to create a new Group called 'Trouble Makers' and I added posters A, B, and C to this group.

For this group I copied the permissions from the User group:
my-forums.Net » Control Panel » Group Management » Site Permissions

I then went to:
my-forums.Net » Control Panel » Group Management » Forum Permissions

and set "All new posts are moderated" for the Suggestions Forum.

I tried both the values 1 and -1 and in either case, posters A, B, and C are still able to post in the Suggestions Forum without their posts needing approval (going into the post queue.)

Anyone see what's going wrong here?

Is member A,B,C a member of any other groups that may have permission? The only way I know would be in the member management section and double check that the member is not in any other groups than Trouble Makers.
Oh while you are editing the member make sure they are not a moderator,Global Moderator or Admin.

The only other groups they are in is Users. If I uncheck this, they can't do anything or see anything. This is why I used -1 in the 'Trouble Makers' group. According to the documentation (heh if I understand it), entering -1 will set (or clear) a permission even if other groups allow it.

So, ...
posterA belongs to Users and Users have "All new posts are moderated" set to 0

posterA ALSO belongs to 'Trouble Makers' and 'Trouble Makers' have "All new posts are moderated" set to -1

Shouldn't all of posterA's posts go into the Moderation queue?

I myself have never tested the -1 value so I can't tell you of all the issues if there are issues.
The problem with what we have now is you can make user groups so complicated that it can become very difficult to keep up with.

To me it would be simpler to keep up with by setting troublemaker permissions the same as user except for post moderation and then delete the member from users.
Of course I don't know the whole picture of what you are trying to do with all of your groups.

Other than that I think you need to put it all down on paper and compare permissions before you start changing them. It may show something you overlooked.

BTW I thought you copied the user group permissions to trouble maker anyway. At least that is what you said.

I did, I used the Copy option to make a duplicate of User Permissions into 'Trouble Maker' group. I then did as you say and just changed the post moderation. Unfortunately this didn't work. I then tried to delete the poster from the User group (leaving him in Trouble Makers) and then they couldn't even see the forum etc.

Thanks anyway Ruben .. It’s a tough one and non-intuitive.
I’m kind of surprised that the ability to moderate particular poster’s posts is so complicated / impossible.

I run a gaming site and I periodically piss off the gamer community by making changes they don’t like. I hate to ban them, so the ability to moderate their posts until they cool-the-hell-off would be the best option.

If they can't see the forum them that is the first option to check in trouble makers group Forum Permissions "Can see forum" in group management. I'll BET THE FORUMS ARE TURNED OFF
I will bet you did not really copy the same settings from users to troublemakers. The process can be a little misleading.
Currently editing permissions for: trouble makers
Copy Permissions from: USERS
Then you need to scroll down to the bottom of screen
Select Update group permissions.

Then go back and see what "Can see forums" is set to. AND SET THE OTHER PERMISSIONS SPECIAL TO THE TROUBLE MAKERS GROUP

Okay, new information:
I redid the whole process of copying the USERS permissions into the TROUBLE MAKERS group and then set "All new posts are moderated" to 1 (not -1) for all of my forums for the TROUBLE MAKERS group. I then went in and removed this user from the USERS group, and added them to the TROUBLE MAKERS group.

And it works
Sheesh!

Thank again Ruben.
Now we know it’s possible (but not for the faint of heart).

Like I said it can become so complicated now that you can't keep track of it. So I try the K.I.S.S. method. Keep It Simple Stupid.
That's for me!
But when you get time you may want to review all the permission settings to make sure they are the way you want.
It is a big hurdle but once it is done it over.