If you haven't tried Zombie Farm on your iPhone or iPad yet, I'm not sure I can recommend that you do so. It's just so addicting. I originally got it on my iPhone 3G back in March and I now continue to play it on my iPad.
If you try it or are a current player, one of the confusing things about it is the mutation system. Hopefully this guide will help. This guide is based on Zombie Farm 0.78.1 released on August 26, 2010.
First of all, mutations are the key to successful invasions at higher levels, so you will want to make sure that you understand how mutations work. Once you unlock a mutation, you can start attempting to grow mutated zombies. This is done by planting zombies next to crops of the appropriate type. For example, for a chance to grow an onion-head zombie, plant a zombie next to an onion.
The timing of this can be confusing. What matters is what is planted next to your zombie when you harvest it. So you can plant a zombie, wait for it to fully grow, then plant your crop next to it just before harvesting the zombie. For purposes of mutations "next to" means that the plots of land touch each other, even if only corner-to-corner.
In this picture, the zombie growing in the middle has eight surrounding plots that are next to it, each capable of causing a mutation.
Zombies are limited to 5 mutations each. This is confusing because the descriptions of the mutations seem to indicate that 6 would be possible. There are six possible mutation locations: arm (you can't mutate both arms), body, collar, eye (you can't mutate both eyes), hair, and head. It appears that the eye and hair are mutually exclusive; you can't ever have both an eye and a hair mutation at the same time, resulting in the 5 mutation limit.
This picture shows how I arrange a zombie-growing section of my farm.
These 10 plots of land allow for growing two zombies, each with 5 mutations: Venus Flytrap Collar (+4 defense), Coffee Head (+2 speed), Cauliflower Hair (+3 defense), Lima Bean Body (+3 defense), and Dragon Fruit Arm (+4 attack).
Headless zombies don't have heads (duh!) and thus are limited to 3 mutations. They cannot have the head, eye, or hair mutations. This can be confirmed in the latest version of Zombie Farm by looking at the stats for a headless zombie; earlier versions made it difficult to know if the head, eye, or hair mutations worked on headless zombies or not.
The Party Zombie shown in this picture was combined from two Flameheads grown in a patch like the one shown above with 5 possible mutations. The stats show that the zombie did not get the Cauliflower Hair or the Coffee Head.
This chart shows all the possible mutations, the effect, the location, and which mutations can be used with others.
In my opinion, the best item to spend brains on is the Mutant Monolith. Once you have this monolith, planting the appropriate crop next to a zombie guarantees a mutation.