What televison programs immitated the storylines of real crimes ie The
Preppy Murderer Robert Chambers or Louise Woodward..shaken baby
syndrome.

Based on the following summaries for this show, I believe it's Law &
Order:

"At first glance, the demise of a baby seems to be a case of crib
death. Upon further investigation, it is revealed that the infant was
poisoned. There is enough compelling evidence to charge the baby's au
pair Lila Crenshaw (Annika Peterson) with murder"
http://entertainment.msn.com/Movies/Movie.aspx?m=531595

"The detectives are frustrated when it looks like a privileged preppie
might get away with killing his girlfriend."
http://www.dickinson.edu/~buchan/season1.html

Also, I thought this paragraph best summed up the show:

"Law & Order episodes are *regularly* based on real-life events, and
always have been. There have been episodes based on the Bernhard Goetz
subway shootings, the Robert Chambers "preppie murder" case, Joel
Steinberg and Hedda Nussbaum, Tawana Brawley, and the Menendez
brothers - just in their first season. Some episodes have multiple
disclaimers, some just have the one mentioned before - that they are
'inspired in part by a true incident.' Being a TV show, though, there
is always some twist to make the story fit their show, and the message
the writers want to send. NBC realizes that intelligent people watch
their show. We know exactly what hot news story the episode is based
on, and also realize that the plot is inspired by, not identical to
that news story. Just because a character does something on the show
doesn't mean that we believe their real-life counterpart did the same
thing. We understand that we're not watching a documentary."
http://www.gooddeed.net/blog/archives/00000156.html

I hope that answers your question.

Another show that uses cases based on real crimes is CSI:

"Are the cases used in the show lifted from real crimes? 

Most of them, yes. Since our writers are real crime scene
investigators or forensic experts, the ideas come from, yes, real
cases. Only the names of the actual persons involved were changed so
as to protect their identities.

Reality TV is the rage today. Is there a conscious effort to align CSI
among these shows to rate better?

No. We just do things as ideas come along. We don't want to make CSI
reality TV although again, most of the cases in the shows are actual
cases."

INQ7.net
http://www.inq7.net/ent/2001/aug/22/text/ent_1-1-p.htm