If I wanted to transmit sensor data from a remote location, such as the middle of the Atlantic Ocean, what would my options be? What are the pros and cons of each? What components are available? (inexpensive components are preferred. Soldering is no problem and even surface-mount would be OK!)
Data rate?
Data volume?
What will be receiving the data? AM radio,100W, might be enough. 4 MHz, 7 MHz, that kind of frequency range. Amateur radio operators take advantage of radio wave bounce off the upper levels of atmosphere for intercontinental communication for example.
Meteor burst was big in the 80s
AWOL:
Meteor burst was big in the 80s
So was my hair, things change 
If you want reliable communication then a Satelite Phone is your only realistic option.
Just google Iridium Satelite Phones.
just spitballin:
Data rate: transmit every 30 minutes, 24/7. baud doesn't matter much as long as it's reasonable.
Date volume: ~1KB or less per transmission
There is less well-known two-way communication of GPS.
Chinese BeiDou GPS's Short message service:
Short message service, also called Positioning Report Service, is supported by BeiDou-1 and consists in allowing the user and the station to exchange short messages (currently 120 Chinese characters per message, double for ascii?). This service will probably be provided by BeiDou and may evolve to longer messages and not limited to position report.
http://www.navipedia.net/index.php/BeiDou_Services
For middle of the Pacific Ocean is working today, but for middle of the Atlantic Ocean is needed to wait.
Here is a review of two satellite-based text messaging services, global in scope.
1kb every 30 minutes is possible over those SMS-type devices but it's a lot of text messages to reassemble at the other end.
The major satphone providers do have modems. 4800baud is a common speed for the basic service. The cost is basically the same as making a phone call over the system. A 10-second phone call every 30 minutes should cost less than the SMS service.