A landline is not necessary to access the Internet. Alternatives to landlines include public Wi-Fi, cellular networks and satellite connections. These methods do have some limitations as compared to landlines, however.
Cities and towns sometimes make public Wi-Fi freely available within certain areas, and public libraries also frequently offer free Wi-Fi connections to patrons.
Some cellular phone plans also include Internet access. MiFi devices that allow users to have a portable, cellular Internet connection without having phone service are also available for purchase.
Satellite connections are possible through services like dishNET. These work similarly to satellite television setups.
All these methods tend to be slower than land-based connections, however, and bandwidth is also generally more expensive.