I've been a fan of homemade instruments for a while now. No offense to the fine instrument builders of the world, but many of us don't need (and can't afford) the very best. Homemade instruments have the added value of teaching how various parts combine to make sound - you don't just learn how to plan an instrument, you learn how to create and manipulate sound-producing materials.
If you've never built anything before, start simple. Drums, shakers, and other percussion instruments can be a good launching point for instrument making. Rhythmweb has some great information and photos on making Sonotube drums and other percussion instruments. Another great resource is the junkmusic Yahoo group with postings and questions by people making experimental instruments.
The most successful of my own experiments is my pineapple mbira, made from a thrift-store wooden bowl, a garden rake, and random bits from my basement.
When you get the basics down, you may want to try some more complex instruments like those built by Iner Souster - see his blog for great photos and sound samples of his mind-boggling creations. I don't know that I wish to re-create the Sunflowers of Death, but I do have some very musical bottles in the basement. And old metal tools. And some quarter-inch plywood. And...