Is there a grid or a table that shows the Amtrak rail distances
between its stations in the north-east corridor?  Basically, trains
starting at Boston's South Station, going through NYC Penn station,
Philadelphia's 30th street station, etc. (those aren't all the stop,
obviously, just the major ones).  If there is a grid or table, is it
available somewhere on the web?

The first table on the page will give you the information you are seeking:

http://www.cwrr.com/Amtrak/ne_bo_nss.html

Hello Rkrikorian,
This information is available from two sources that I know of.  The
first is Amtrak of course.  If you go to their site at
http://www.amtrak.com you should be able to download maps for all of
their routes.  You can also try http://www.vacationsbyrail.com for
route maps that include many popular US destinations.  Many of the
East Coast routes can be found at
http://www.vacationsbyrail.com/usa/amtrak_vacations/new_york/index.html.
 Vacations By Rail specializes in rail vacation packages, so if that
is what you are interested in you should really take a look.
Regards,
Lars Belmans
Vacations By Rail