JMP has long had the Internet Open command in the file menu, and similar functionality is available through JSL in JMP 7. Specifically, you can now pass a URL to the Open and Load Text File operators. Here's an example that reads crop data from the USDA site. The result is a Comma-Separated Values (CSV) text stream, which JMP opens as a data table.
Open( "http://www.usda.gov/nass/graphics/county04/data/aw04.csv", text );
Some web sites implement RESTful web services where the URL contains query fields, and the result is an XML or CSV file. Here's an example of using such a service from Yahoo Finance to get historical stock prices.