Head to your greengrocer or supermarket and ask if they have any deep polystyrene boxes to give away. These make great vegie gardens. Fill them with potting mix and use them to grow all sorts of vegies including beans, carrots, tomatoes and cucumbers.
Hang 'em high
An effective way to grow lettuces is to use one of the 'multihole' hanging baskets. Just plant a seedling in each of the holes and watch them grow. Balconies are great for growing herbs as you can hang the containers so they take up no floor space.
You can grow almost any vegies in tubs. Try tomatoes, carrots, parsley, garlic, onions or lettuces for starters but you can even use them to grow climbing vegies such as beans or peas. All you need is to put up some trellis against a wall. Your vegie tubs don't have to be expensive - plastic terracotta pots look nice and are quite cheap too.
Roll out the barrel
I made terrific container gardens by purchasing some old wine barrel halves from my local nursery. They're huge and deep, so are perfect for growing vegetables. But if they're going on the balcony, just check the balcony's load bearing capacity first.
If you don't have enough space for a garden of your own, but would love one, look at the possibility of a community garden in your area. Phone your local council to find the nearest one.