If you simply want the material on Site A to be seen on Site B you could try
setting up a content deployment job that would push the material from Site A to
Site on a schedule. If you need the material to be updateable on both sides,
however, this way won't work because content deployment is a one-way trip.

Assuming that changes can be made in either Site A or Site B your only real
choice is one of the commercial synch programs. Syntergy
(http://www.syntergy.com/sharepoint%5Cproducts/replication/ )makes a product
called replicator and Infonic
(www.infonic.com/...s_sharepoint_geo_replicator.php ) makes a
product called Geo-Replicator.

If changes are only made on one Site, then you could use the OOB MOSS Content
Deployment capability.

If you just want to synch several lists or libraries you could use a combination
of event handlers and XML web  service calls.

Cross-site, yes. Cross-server?...I don't think so. I suspect that you are
limited to using a Page Viewer Web Part and poking in the URL. Even the
third party vendors don't offer that.

What information  are you trying to share? You can query all sorts of
stuff using the web  services provided. It would require development of a
custom web part but I don't think what you are trying to do is
impossible.

Content deployment certainly works across server and across farm. The drawback
to using content deployment would be if you wanted to be able to modify the data
at both ends. This you could not do. The data is only editable at the source,
not at the destination. If you wanted to do more you would need to look into
some of the solutions.

Clearly I need to pay more attention. I wasn't even aware that this could be
done.

As penance for my sins, and to help those that are similarly clueless,
here's a few links.

Planning Content Deployment
technet.microsoft.com/en-us/library/cc263428.aspx

Content deployment topology
technet.microsoft.com/en-us/library/cc262004.aspx

Worksheet for Content Deployment
http://go.microsoft.com/fwlink/?LinkId=77804
<http://go.microsoft.com/fwlink/?LinkId=77804&clcid=0x409> &clcid=0x409

Deployment Tutorial
blogs.msdn.com/.../content-deployment-step-by
-step-tutorial.aspx

Wizard for Content Deployment (I haven't tried this, but it looks
interesting)
http://www.codeplex.com/SPDeploymentWizard

I am not sure how you want to display  the information, but you might try
connection to the other server via the moss web  services and pulling the
information in that way.