Get to know parlour games. These games are a dying tradition, but there are books and web sites that describe hundreds of examples, many of which require no props, and can be played by groups of all sizes. But someone has got to know the games and how to play them. Be that person!
For groups of three to twelve (ish), one of my favourites is "Two Truths And A Lie." Each person takes turns making three statements about themselves: two must be true, one must be a lie. After saying their statements, the person falls silent, and the rest of the group discusses until they reach consensus about which is the lie. It's a good icebreaker, even for people who know each another well.
There are word games galore that require no or few props, including "Oh, no, no, no" and "Mime Rhyme." You need a dictionary to play "Fictionary" plus pens and paper. It's one of my all time favourites.
"Music Magic" is hard to categorize, but unbelievably surprising and fun:
1. Someone volunteers to be "It," and leaves the room or the area.
2. The group decides on a complex action they want "It" to perform, e.g., Enter the circle of people at this point, touch the bridge of your nose with your left baby finger, skip across the circle backwards, turn around to face the opposite direction, and start doing jumping jacks while meowing.
3. The group chooses a song everybody knows, e.g., Happy Birthday; and invites It to return.
4. The group sings the song more loudly when It is getting closer to performing the desired action, and more softly when It is doing the "wrong" thing. Guided by the song, It must discover every move, in the right sequence.
Witnessing someone figure out the target actions, guided only by a song, is hilarious. When the game is introduced, many may not believe it's possible. Yet some people figure out the steps very quickly. When the end is reached, people are singing so loudly they are almost hoarse!
A variation: the group members clap (loudly or softly) instead of sing.