Many times the glue in such joints ages and becomes loose. This is common. Sometimes it is just a matter of taking the joints completely apart, remove the old glue, apply new glue, and put the chair back together. The chair should be clamped with all of the joints tight for at least 12 hours.
In more severe cases, where there are large gaps in the joints, an epoxy filler can be used in place of glue, or thin wood shavings can be wrapped around the ends before they are glued and put back into the matching holes.
Furniture repair shops do this work all the time, if you are not comfortable with it. I own a Furniture medic franchise in Colorado, and there are others all over the US. Check out www.furnituremedic.com, or your local business directory under furniture repair.
Furniture Medic by Randy Buchter
January 2012
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix chairs.