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Cordless Datalink
Once you find a landline phone to connect to, the next hurdle is how to get to it. I generally carry a 100' cord I picked up at Radio Shack, but another option is the Panasonic Datalink. The going price seems to be somewhere around $200. It's like an electronic walkie-talkie, with one part connected to the phone line and the other part plugged into from your laptop. The one I've used is good up to about 100' and seems to work as well as the real line. The major advantage is not having to string the 100' cord through your friend's house, campground office, etc. The 2.5 hour recharge limit is a bit of a problem, but can be overcome by getting an extra AC plug. Click the picture for details on the datalink.
Laptop-to-Cellphone
Another method for doing all of the internet things mentioned above when you can't find a landline phone to borrow/rent is to set your laptop up with a modem (about $400) that will connect to your cellphone. Of course, you'll need a cellphone service that provides you with a substantial amount of free time in order to use the connection for enough time to do anything online. Also probably one with free long distance and roaming, assuming you're planning to travel outside of your home cellphone area. Finally, you'll need one of the cellphone antennas in order to maintain a strong enough signal to hold the internet connection.

I purchased such a setup from Radio Shack and have been quite pleased with the performance. You can get about 9600 baud when close to a large city and 4800 when out of town. This is substantially slower than the 33,000 to 56,000 possible with landline connections, but is fast enough to do email, surfing, shopping, and investing -- and maybe a little website-building if you don't get too ambitious.

I'm currently checking availability of setups from other vendors and will update the information here with some links as soon as I finish.

April 2006: There are now internet options with most cell phones, but I haven't taken the time to check into them regarding cost, access speed, coverage, etc. As I get more info, I'll add it here and put a note in the news section on the main page.

2003 UPDATE: Found the modem card, noted above as costing about $400, for only $139.95. I haven't  tried the product myself, but it comes with a five year guarantee, so sounds like a great possibility. The product is manufactured by Ositech and is sold by many distributors, including DiscountCell. Below is the ad from their website:
Laptop-to-Temporary Phone
The cheapest way to get email, surfing, website-building, shopping, and investing is using a borrowed phone at a campground, Kinko's, etc. -- assuming you already have a laptop. I omit games and chat, since most of the available connections that I've found wouldn't allow you to stay online long enough to play any games or spend much time in a chatroom.

For several pages of suggestions on where to find free phones and "rentable" phones, click on the antique phone. To return, look for the yellow box with the wireless internet picture.
Click to go to DiscountCell
Ositech King of Clubs Cellular Modem Kit with CELLFLEX

Diagnostic and Installation Wizard 
Motorola or Nokia Cellular cable provided
CellFlex Dual Mode Data technology (phone models in Red) allows phone to connect to data source in digital mode.
Automatic detection of landline or cellular operation
Automatic detection of home or roaming network
Support MNP 10-EC (Error Correction) for improved cellular operation 
Flash Upgradeable ROM 
Can be used in Macintosh and Linux environments 
Free Technical Support 
Compatible with Nokia 5120, 5120i, 5125, 5160, 5160i, 5165, 6120, 6120i, 6160, 6160i, 6160m, 6161, 6161i, 6162, 6162i, 6162m, and 7160

Manufacturer: Ositech

$139.95
Internet-On-The-Road (IOTR)