Annoyingly, MAMP will override your favicons. This can be annoying when you really need to quickly identify tabs!
To stop this behavior find the following file:
And then comment out the following line:
#Alias /favicon.ico "/Applications/MAMP/bin/favicon.ico"
This works for the standard, free version of MAMP — which is what I use.
Hat tip to Tim Neil who first discovered this while using MAMP Pro.