There are a few rules to follow when deciding what to give them, but in general you can feed them most things.
Things To Include
Fruit and veg peelingsWaste fruit and veg
Plate scrapings
Mouldy stuff from the fridge- e.g baked beans, salsa dips....
Small amounts of bread
Small amounts of pasta
Small amounts of rice
Small amounts of chicken droppings
Cake (but why would you want to throw this away?)
Cereals
Citrus in small quantities
Cooked egg in small quantities
Things To Avoid
Garden waste - for the following reasons1) You will most probably have a council collection for this
2) The very brown dry twiggy stuff which makes up most garden waste is too hard for worms to chew on and will just stay there in it's original form for aeons.
3) Grass is not good in wormeries, as it quickly turns to mush and goes black and horrid before your worms have a chance to munch on it.
Raw meat, fish and dairy - These are best avoided, because they will quickly go rancid before the worms have a chance to eat it.
Dog and Cat poo - it's nasty smelly stuff and can carry diseases, so it's best disposed of in a knotted carrier bag in the dustbin
Pickled foods - pickled foods will not rot down quickly, because pickling preserves foods. They may effect the pH levels of your bin making it an unpleasant environment for your worms.
Things To Avoid
If you have given your worms an abnormal amount of scraps, they will be struggling to keep up. This could slow down the composting process, resulting in rather unpleasant looking contents and the possibility of fruit flies. Although fruit flies are harmless, they are a nuisance, and unfortunately they like all the same foods that the worms like. So make sure you don't overload your Hungry Bin!
Over-feeding will result in an unhealthy Hungry Bin!

Fruit flies will lay eggs in rotting food.