Besides using barre chords to play in different positions up the neck, or playing in open tunings, another way to add a little variety while playing along is to capo up a few frets higher than the song leader (or, if the leader is playing with a capo, play in open position if possible or capo at a lower position). Same basic principle as using barre chords, but easier on the fingers...

Admittedly, this is relatively advanced advice ~ "Playing Along II" ~ but it's certainly an idea worth mentioning. One of course needs to be able to recognize the chord changes in a simple song and understand how to transpose keys, concepts many of us can handle and which all of us can reasonably hope to learn. (I can't take credit for this one, by the way; as many of you probably recognized already, this is a bit of advice that has often been put forward by Kevin McGrath of Harlow.)

Having a large number of instruments strumming the same (full) chords on the same beat is not always termendously interesting ~ especially when most or all of the intruments are guitars! (Of course, it's far preferable to hearing the wrong chords played not on the beat...) While the beginnners in a group should not be discouraged from doing their best with a simple approach, the overall sound and appeal ~ and fun! ~ of a group jam is greatly enhanced when those who are able can introduce some variety by:
~ playing in different positions on the neck; or
~ fingerpicking patterns of single notes rather than strumming full chords, or
~ (something no one has mentioned yet) playing single-string fills or runs between (i.e., in response to) the sung lines.