How can I fix a big crack on an old hutch?
It will be difficult to replace the whole side but it doesn't appear to be necessary anyway since the crack seems to be mainly cosmetic.  Since the piece looks like it is painted this is what I would do:

Use a bar clamp across the width of the case to snug up the crack as much as you can.  (If it will close all the way then also put glue in with a small brush.  Unfortunately if there is old glue then the new glue is unlikely to hold well.)  With the clamp holding the piece in place drill countersunk holes and secure it with a couple screws.  

You can buy wood plugs or use short lengths cut from a wood dowel to cover the screws.  I would have the plugs on hand so you know what size you need to match when you are pre-drilling for the screws.  Or, you could also just use bondo or other filler to cover the screws instead of the plugs.  As long as the screws are holding the pieces fairly securely you can also fill a small remaining crack with the bondo / filler.  Sand the filler and repaint.