I have a simple armature that has three loose bones that I would like to join at one joint. Is there a way I can join these 3 into a single joint?
You can join multiple bones together. You will need to flip one of the bones around (AltF) so that there is a bone tail in the correct spot. Then just set the other two bones' parent to the flipped bone; and enable Connected.
Create a control bone; Make it small. Basically you need to create an extra bone that all of the others connect to. Although you must create it, you never have to use it in posing. (It can still be useful.) The small end of this bone needs to be facing toward the other bones.
Here is a picture of the control bone created properly and positioned with the little end at the spot that you want the new joint to be.
Create the master joint; Turn on Vertex Snapping down at the bottom of the screen; this will allow you to position the bones perfectly at the location of the master joint. Here’s a picture to help you find vertex snapping.
By default the snap mode is increment. Change this to vertex by clicking the option tab and selecting the vertex option (cube with white dots).
Select one of the joints.
Mouse over the small end of the control bone, and press G. Move the big joint to the little end of the control bone.
Repeat this for the other two bones.
Parent the bones; If you've followed the steps alright, you should have something that looks like this:
Select the three bones that you want to make one joint of. Then select the control bone. Press Ctrl+P>Connected
Boom!; You just made one joint out of three!
It appears that this is not possible unless they are part of the same chain. As the Blender Wiki states:
You can merge together several selected bones, as long as they form a chain. Each sub-chain formed by the selected bones will give one bone, whose root will be the root of the root bone, and whose tip will be the tip of the tip bone.
For further information, read the original documentation on the Blender Wiki.
The snap functions can be used in Edit Mode to set head or tail of the bones. Shift-S Cursor to selected and Selection to cursor could be used to align them.
You can join bones like any other object using Ctrl-J after that the Parent-Control in the bones properties will be available.