Note: I published this instructable in 2010, but unpublished it while I developed it further as a submission to the American Chemical Society's Journal of Chemical Education. The article has now appeared, so for those of you who happen to have electronic access to this journal (probably because you are connected through a university network), you can find the manuscript online here.
Step 1: Ingredients
Sprite (or other clear carbonated beverage) ~ baking soda ~ red cabbage ~ citric acid ~ tap water
Step 2: Red Cabbage?
To get the indicator, you can chop up a cabbage leaf and microwave it in a small amount of water, or add boiling water, or blend and strain the cabbage leaf (thanks to groenert for this last tip). You should get a deep purple-colored liquid.
Step 3: Build
Add about 1/4 teaspoon of citric acid to a teaspoon or two of water, and stir until dissolved. Add it to a half-filled glass of Sprite (or similar).
Step 4: Serve!
Adding the clear Sprite to the blue solution works well, too, and if you watch closely you can see it transition through purple. Also, substituting sugary water for the Sprite works fine. Here's a video of these two together (sugar + citric acid + water added to cabbage juice + baking soda + water):
Pouring them in simultaneously from small glasses into a bigger one also looks good.