I'm looking for a free or cheap program that will allow me to "watch"
my PC's Internet activity. I want to be able to "see" what programs
are sending/receiving data over my connection at any given time and
perhaps even what the programs are connecting to and/or
sending/receiving.

Generally, what you're looking for can be divided into two groups. 
The first type is a firewall, which would allow you to control which
programs on your computer can talk to the Internet and how other
computers on the Internet can talk to yours.  These are available in
both software and hardware form, although only the software form
allows you monitor which programs on your computer are talking to the
Internet.

A common, popular software firewall is called Zone Alarm, and it is
available at www.ZoneLabs.com.  Both free versions and paid versions
are available. This product would allow you to see and control which
programs on your computer are communicating with the Internet, but
does not offer any additional information about what specifically they
are communicating about or to whom.  McAfee Firewall, available from
www.McAfee.com for about $30, allows you to see what IP address
programs are communicating to and how much data has been sent, but
does not allow you to see what has been sent.

The second type is a packet sniffer, which allows you to examine
network traffic in detail.  A packet sniffer doesn't allow you to
control anything, but allows a great deal of monitoring of the type
you appear to be requesting.  Here is a link to several free packet
sniffer software programs:
http://netsecurity.about.com/library/blfreepacsniff.htm

One of the programs available from the link above, or directly via
http://www.securesphere.net/html/projects_sniphere.php is Sniphere. 
The description of this program sounds like it could be of great use
to you, and suggests that it would be relatively easy to use.

Ethereal is another popular free packet sniffer, also available from
the link above, or directly via http://www.ethereal.com

Here is a link to a set of trialware packet sniffers, most of which
appear to have limitations of 15 to 30 day trials before requiring
purchase in amounts of about $100:
http://downloads-zdnet.com.com/3150-2001-0-1-0.html?qt=packet+sniffer&tag=new

I hope that one of the above programs meet your needs.

Sincerely,

Wonko

The following free program may be of interest. It's called TCPView and
it shows all the TCP/IP connections your computer has established. If
you have Windows NT, 2000, or XP it also show which programs are
connected.

  TCPView - Sysinternals Freeware
  http://www.sysinternals.com/ntw2k/source/tcpview.shtml


Another free program from this site is called TDIMon. It appears to be
similar to TCPView but provides more details about each connection.

  TDIMon - Sysinternals Freeware
  http://www.sysinternals.com/ntw2k/freeware/tdimon.shtml