My computer network is showing that every packet is transmitted twice
and every packet is acknowledged twice.  For instance, if I open
Outlook, a traffic sniff will show that each packet shows up twice.
This is true for our ENTIRE network.  Performance is okay for now, but
we obviously want to cut down on these duplicate IP packets.
We just installed a Cisco 6500 switch which has greatly increased
performance, but, this issue just started after we installed the
switch.

I assume that this is a multi-switch environment and they are
connected in a redundant path.  I believe that your problem is that
you multiple active paths between the switches, which is causing
loops.  If a loop exists in the network, you might receive duplicate
messages.  When loops occur, some switches see stations on both sides
of the switch. This condition confuses the forwarding algorithm and
allows duplicate frames to be forwarded.  Make sure you have the
spanning tree protocol (STP) enabled on all VLANs.  The default
configuration has STP enabled for all VLANs.

We finally figured this one out.  The span session was set on a port
within vlan 100.  We were capturing traffic for vlan 11 and vlan 100,
therefore receiving duplicate packets.  It seems odd that Cisco would
not override this on the 6500 series switch, but it seems that is the
case.  Span sessions should be created on a port "out of" a vlan
because span does not pull the port out of the vlan itself.