Well, there's the Outlook Web Access web parts that you get out of the box.

Lastly, I wouldn't say this is connecting as much as copying, but you can synch
a SharePoint contact list to Outlook, then from Outlook drag and drop your
contacts into that list.

You can expose a local outlook  client mailbox using html code. (With or
without sharepoint)

Just specify the folder parameter as "Contacts"

<OBJECT classid=CLSID:0006F063-0000-0000-C000-000000000046

id=ViewCtlFolder

width="100%"

height="400"

codebase="https://activex.microsoft.com/activex/controls/office/outlctlx
.CAB#ver=9,0,0,3203">

<param name="Namespace" value="MAPI">

<param name="Folder" value="Contacts">

<param name="Restriction" value="">

<param name="DeferUpdate" value="0">

</OBJECT>