I like an ancient tool called iptraf. It shows realtime connections I'm hitting and where they are going.
http://iptraf.seul.org/download.html
You didn't tell us what OS you have, but most have that app packaged in a repo somewhere.
Thanks for the responses everyone ! I think it was an early version of iptraf. The current one uses ncurses but the version that I started playing with was text based only. If you look at the current version (http://iptraf.seul.org/shots/iptraf-iptm1.gif) you will see the screen divided up into two parts. The top part shows you your current connections while the bottom shows you a log of connection attempts. Back when I first started using this the bottom part was the only part that we had. We used to redirect it's output to a file and then tail it and have it show on the desktop background. Good times :) Thanks for all the help everyone; I truly appreciate it. And Happy Holidays if you are celebrating.
Windows will itself tell you how much bandwidth it has used -- double-click the interface for packets sent & received details, subtract start of day figures from end of day figures. As long as no reboots occur!
Otherwise set up iptraf on a linux host and away you go.
For server I use IPTraf which is a console-based network statistics utility that gathers TCP connection paket and byte counts, interface statistics, and activity indicators - http://iptraf.seul.org/
For desktop I've installed Netspeed applet that displays information on the traffic on the specified network device such as in and out of traffic.