Back before I had my iPhone years ago, I used a normal flip phone that could get online if I wanted to but had no data plan. I never used the web on the phone because it really sucked for that use. However, on more than one occasion I accidentally launched the browser while trying to do something else. You can't close that browser until it connects and downloads its data and by that point, you are charged for data use even if you don't have a data plan.
Verizon Wireless is in some hot water over just such a practice and has announced that it will be issuing its users up to $90 million in refunds. The refunds will go out to 15 million former and current customers of Verizon. Those eligible for the refunds that are still with Verizon will see credits to their bill in the range of $2 to $6 though some may get bigger refunds.
The refunds are for data charged at the $1.99 per megabyte rate for users not having a data plan. The improper charges for the data have been occurring since 2007 and the FCC has reportedly received hundreds of complaints. Verizon may have to pay penalties as well for the improper billing to its customers.