This is a very big Fibonacci site in the UK. It has a lot of discussion of rabbits, cows and bees and also terrific photos of veggies, flowers, and pinecones.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
This site includes Fibonacci puzzles. Try some.
http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpuzzles.html
Also there are some Quicktime movies of spirals growing on this site. Oddly enough so far I can only find them linked from another site:
http://www.geocities.com/CapeCanaveral/Station/8228/pineandsun.htm
Some nice measuring ideas for kids - also additional links
http://math.rice.edu/~lanius/Geom/golden.html
The UBC page is also aimed at young students.
http://www.math.ubc.ca/~hoek/Teaching/Golden/Divina.html
Dr. Math has some discussion of Fibonacci basics and some more links.
http://mathforum.org/dr.math/faq/faq.golden.ratio.html
This phyllotaxis site has amazing applets that draw some of the spirally steps that we tried in our conversation about the rules of growth.
http://www.math.smith.edu/~phyllo/