For Board meetings: When I was president, I asked each member to introduce themselves and tell us how many children they have and what grades they were in. (every mom loves to talk about her kids). The theme for our first training meeting was "What's in your purse?" (or wallet, if you have dads) We played a quick little game of having all the ladies grab their purse and find a series of items in them at my request: "An item that absolutely should not be in there" " A sweet memory" "Something green" "Something from one of your kids"--you'd be surprised what people come up with. Before long everyone's laughing and relating and communication becomes easier.
Then I'm able to get to some great encouragers that I've "planted" in my own purse/tote bag. I write large words (example:TEAM WORK, COMMUNICATION, TIME MANAGEMENT, POSITIVE ATTITUDE) on construction paper that will help our special team throughout the year. It's a great time to talk about expectations and responsibilities as well as addressing anyone's questions or concerns. It may take 15 minutes out of your meeting, but my team said they greatly appreciated it.
We have had success with "Hello, That's Me" - the president or the meeting leader starts by telling about her/him self and when a audience member hears something that connects they say "hello, that's me" and links elbows with the leader - then he/she begins to tell things until another person hears a connection - pretty soon everyone is connected which gives a good illustration as to how we all are connected in some way to each other.
Another activity that has worked for me is to have everyone line up by first name alphabetically (sometimes do this by telling them no talking which really makes it interesting) - then we "test" by going down the line giving first name and telling one unique or interesting thing about themselves (I find this helps people remember names especially when you are working with a group that has new members in it).
When we had new people that were not aquainted with one another, I have passed out pennies and each person had to tell something about themselves that had to do with the year that the penny was made. It got really funny toward the end.