I use the Internet while I travel and take a netbook with me. Mainly making bookings and doing research but I like to keep in touch with my family via Skype.
If we are traveling thru a number of countries I would use free wifi from some libraries or buy into Internet cafes or hotels. If you are doing Internet banking don't Internet cafes make sure you have a secure line.
If I am traveling for say a month or more in one country I buy a dongle with service this gives me 24/7 availability and is more secure using my netbook if I am Internet banking.