Of course it depends upon the mix of people you have at any gathering, but off the top of my head, here are a couple of activities that have worked well at breaking the ice. They are all things you can do at the last minute with minimal preparation:
1. Ask each person in the group to think of two true facts about themselves, and one lie. Each person in the group takes a turn telling the group their three facts.
The group then has to agree on which fact they think is a lie. Once the group announces their decision, the speaker tells the group the correct answer. The group then can talk about any of the interesting things they just learned about the new person.
2. Have everyone stand in a circle. One person stands in the middle. Give them time to ask the names of the players on either side of them.
Once the names are known, the person in the middle goes up to a player and says "(name)___, bumpity bump bump bump." That person then has to say the names of the people sitting/standing beside him/her before the middle person finishes saying "bumpity bump bump bump."
ADDED TWIST:
The person in the middle can randomly yell out bumpity bump bump bump and everyone has to find a new spot in the circle.
3. Have name tags of famous people or fictional characters. As people arrive place the name tag (without letting them see it) on their BACK. They then have to speak with other people and ask questions to try and guess who they are. When they guess correctly they may move the name tag to their front. They can ask pretty much anything except they cannot ask someone to just tell them who they are.