If a mobile device can access the internet through a wireless network it is considered web enabled.
Any product which can be used with the world wide web, regardless of whether it is mobile or not, can be referred to as a web enabled device too.
This can either entail accessing a web browser or by connecting to other applications that can synchronise data.
Most modern technology is web enabled, and more is being introduced almost daily it seems.
The latest thing seems to be wearables, though these are not truly web enabled because most of them rely on a smartphone which is the web enabled component.
There are watches that have their own sim card and can access the internet independently, but the question then is, is that a watch or a phone? Wait for it, the Photch with be with us soon! :-)
The "internet of things" is another concept you might be interested in. It refers to everyday objects (from refrigerators through to smoke alarms) being able to connect to the internet, and therefore communicate with other devices or with us!