What OODBMS are available for PHP? I need an OODBMS for my website, to handle hierarchies and inheritance.
I use PHP and I have a feeling I am asking too much and will have to do with regular RDBMS...
My personal opinion, is that there isn't much sense in using OODBMS over RDBMS.

Due primarily to a lack of a standard language, comparable to that of SQL, OODBMS are often niche, proprietary, commercial systems. You'll be hard-pressed to find a viable option for a language like PHP because of that. You'd probably have better luck finding something if you were using Java or C++. I did find this comparison table, which might be of interest to you; though it looks like it was last updated in 2009; so be mindful.

Perhaps you could consider instead, a RDBMS + ORM solution using Doctrine.