For a different view from the rest of the replies: our family takes a more relaxed view of things. Shabbat is for food, family, and taking time off from the hustle and bustle. This may include things like:

* Scrabble and other board games

* Cycling and other outdoor activities

* Reading

* Gardening

* Picnicking with friends (though not so much nowadays)

We don't really subscribe to the very strict definition of "work", and I don't think the rest of our synagogue community does either. But phones, internet, and computing are largely discouraged.