People often feel better after they've had a good cry.  is there a biological reason for this?  

Neurotransmitters. I don't have proof, but i would venture to guess that it has something to do with a serotonin bump that comes from the emotional purge of crying. Increases in serotonin help mood, which is why medicines that increase serotonin levels in the brain (like prozac) are effective in treating depression.
Yes, but. Yes, i believe there is a biological reason for this, but there haven't been sufficient studies to truly understand the mechanism. The serotonin hypothesis for mood regulation is incomplete. Work is being done with function MRI to understand the neural networks involved in emotion and it offers more compelling theories. Remember, the brain is an electro-chemical organ.