Curves following bones?

You have a few options. There are others depending on the type of curve and what you need it to do. Here is the main ones. 

First is to use armature modifier. Select curve, shift+select armature, Ctrl+P->With Envelope. Depending on your version it may have the bug where it doesn't check Bone Envelope on the armature modifier. So make sure to check it. Envelopes can be tricky and in my limited experience is rarely what someone needs for rigging their curve.

Second option is to use the hook modifier. There are 3 ways to go about assigning your hooks. 
1. Hook straight to bones(My recommended way). Select armature, ctrl+tab to pose mode, select bone to hook to, ctrl+tab to object mode, shift+select curve, tab into edit mode, select control point(Also called vertex), press ctrl+h->hook to selected bone, tab back to object mode and repeat for next one.
2. Hook to empty and parent empty to bones. Part 1: Select curve, select control point, press ctrl+h->New object. Repeat for each control point. This will create an empty at the control point's location and hook it. When done tab back to object mode. Part 2: Select armature, Ctrl+tab into pose mode, select bone, Ctrl+tab into object mode, select empty, shift+select armature, ctrl+p->Bone. 
3. Manually assign to hook modifier. Select curve, go to modifier tab in the properties editor, add a hook modifier(It's under deform) for each bone that you plan to hook to a control point. On each modifier, select the armature as the object then select the bone for that modifier.  In 3D Viewport, tab into edit mode, select the control point and then on the modifier click the assign button.