Basic requirements
The only essential requirement of a container is the ability to hold compost - enough to avoid drying out too quickly. Drainage holes are desirable to allow surplus water to escape and prevent waterlogging.
See Window Boxes for a step-by-step guide to making your own window box.

Unusual planters
Wicker baskets: As long as the basket is strong enough, any size will do. A plastic liner with drainage holes will make the basket last longer.
Zinc baths: These give an attractive alpine look. Be sure to put in plenty of drainage holes before filling with compost.
Painted wheelbarrows: These look good and have the advantage of easy portability.
Buckets: Add drainage holes a few inches above the base to provide a reservoir of water.
Large chimney pots: Make attractive rustic focal points.

From the kitchen
Teapot/kettle/jugs: It can be difficult to make drainage holes in these sorts of containers, so are best used for water plants.
Colander: Useful for plants requiring good drainage!
Milk bottles: Paint with an opaque paint to disguise the compost. As drilling holes in glass is difficult, water sparingly.
Egg cups: These can be a fun way of supplying fresh cress for your egg sandwiches!

Zany ideas
Bin liners: Tie into a sausage shape and plant strawberries or bedding plants through the holes.
Old shoes or clogs: Plastic shoes are better than leather as the latter will go mouldy, and well-worn shoes should come with their own drainage holes!
Children's toys: Try planting a plastic pram - useful for a first garden and can be taken for walks.
Bricks: Use one with three central holes, insert compost and plant with cacti.
Bidet/lavatory: Definitely for the more adventurous garden! Try planting with trailing plants to hide the container.
Cow sculls: Scrub out well before planting - cacti look good in these.

Have some fun and test out your green fingers with the UKTV Style virtual window box at Grow for it!