Push rod is bent on 16 hp briggs and stratton - what are the possible causes

Hi,
Moved your post to separate from a 3+ year old thread; only way it is liable to get noticed!
Two things would be sheared key causing a timing error, or stripped camshaft gear causing piston to strike valve when open because of a different type of timing issue.
Peace,
Clarke

I found on one the valve guide in the head moved and caused it to bind up and bent the push rod...

Hi,
That happens, but the cause of it coming loose is generally fuel or heat related. Usually to second because of expansion of dissimilar metals at different rates.
Unless you have a Vanguard, it means a new head under most circumstances.
Peace,
Clarke