Here are the ingredients you should be  avoiding:

Casein (a milk protein)
Whey (dairy fat)
Cheeses
Butter
Cream
Milk
Ice Cream

Some ingredients list "Natural Flavorings" as an ingredient.  Sometimes, these "Natural Flavorings" contain dairy products. This is becoming less of a problem as dairy has become a known allergen and is usually listed if it is present.
Watch out for packages that have "May contain dairy" written on them.  It isn't always in the front of the package, but usually by the ingredients.
Also, most margerines contain dairy. Click for a list of
my favourite dairy alternatives which lists a good dairy free margerine.
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