I believe Chop uses DirectWay Satellite internet for his connectivity. If you do a lot of ssh (secure telnet), then satellite isn't going to be enjoyable. ICQ, email, surfing is all ok because of the packet based nature, but, the latency is going to be high. I don't think you could use services like XBox live, World of Warcraft, etc because of the high latency. I also think that vonage/callvantage/skype, etc would also not work well over satellite.
Depending on where you are and how remote you get, there is also GPRS/Edge service through cell providers. Again, these companies don't understand the word 'unlimited' so, you'll find these to be somewhat costly. I believe
http://b2b.vzw.com/productsservices/wirelessinternet/ does work pretty well. Cleo has had some experience with it.
Dialup & using your cell phone as a modem also work but are usually limited speeds. But, you can't be as 'remote'.
For even more remote, vsat services do work, but are very expensive. Like Jim said, the expense of those units is the positioning. However, Hughes does manufacture a 'flat' dish that can be mounted on a rooftop so that you can get satellite TV on cars. I believe you're looking at a few thousand for that + service. There are other solutions. Remember that satellite only covers a portion of the world with a signal, so, you might need multiple service providers depending on where you travel.
I believe GPRS/Edge probably holds the best chance of giving you what you want, but, its not unlimited. Coverage is pretty good -- including the caribbean, parts of Mexico, a good chunk of Canada. If you used signal strength to determine how far off the beaten path you wanted to go, you could still get relatively decent internet connections.