Depends
Take the stereotypical slow BRAINS zombie. They are driven by an uncontrollable desire and have no other goals but to get more brains. Many undead are like this, even intelligent skeletons.
However, any undead beast which can make moral choices on any level must have a soul.
Take vampires. They need blood, sure, but they can choose who they attack, and the may have standards (avoiding children, whatever), and they certainly can hold a conversation. Vampires must have souls.
However, there is still the case of undead beings which have sold their soul, or had their soul taken over by a powerful magician or whatever.
In these cases, they still must maintain a fragment of their soul or the whole process would have been meaningless. However, they are also driven by the rulership of their masters. In this sense, they lack a soul to make choices on their actions if their master makes a demand. The master taking part of the soul is what allows him to do this without fear of the undead rebelling.
So I say undead can have no soul, in which case they aren't really even true undead - they are just mindless bodies of mechanical and physical desires. Undead can maintain their full souls, in which case they are more like normal humans or beasts that are cursed. Or undead can have their souls controlled, in which case they may act normal most of the time, but be "sleepers" for dark forces to act upon.