Some hotels charge up to $15 a day for wireless or high-speed Internet access and some offer it for free. But you need to do your homework to find our whether this access is secured. On travel sites such as Expedia or Orbitz, you can scroll through a hotel's "features" list to see if there is a fee for Internet access.
A quick search on the Internet for "free hotel Wi-Fi" also reveals that chains such as Onmi, Kimpton and Microtel offer free wireless Internet access for guests. The site TravelPost has a section called "Hotel chain Internet Access Guide" that lists which major chains offer access for free or for a fee.
Be aware that "Wi-Fi" access may not be secured in hotels -- ask before you make a reservation. If you don't want to take chances with your data, many hotels offer wired Ethernet connections to rooms, which tend to be more secure and less vulnerable to hackers.