The Zerg are actually composed of several different types of creatures ("breeds") which, while physically distinct and unrelated, seem to share a common psychology and sense of community. They are extremely aggressive and almost cruel in their attacks and attempts to infest inhabited areas. Species that they encounter are either deemed useful to the hive and mutated, or eradicated.
It would be hard to determine the full extent of the Zerg intelligence, but it is clear that they are a very cunning species, and they are capable of higher reasoning. Although they do not use technology that we know of, they demonstrate a clear understanding of it, and have been known to open airlocks and doorways in colonies that they have raided. As a group they also react intelligently to attacks and are adept at tactical combat. On an individual basis, though, the Zerg seem to be hardly more than savage animals with little or no concern for self-preservation.
The Zerg as a whole are extremely tough, tenacious, and deadly. Their natural armor and weaponry is comparable to modern technology in terms of toughness and armor-piercing capabilities. They are extremely resistant to radiation and chemical agents, and possess an incredible regenerative ability and accelerated growth rate. Great care must be taken to completely destroy any Zerg encountered, or they will return in full health.