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Wolfram's listing of all 256 elementary cellular automata reveals some intersting patterns. For example, the first column shows that starting from rule 0, every eighth rule generates one of only two patterns, whcih occur in pairs. That is, rules 0, 8, 32, 40, 64, 72, etc. all create a single pattern, and rules 16, 14, 48, 56, 80, 88, etc. all create a different single pattern. This 'pattern of patterns' could be described, considering only those rules which are multiples of eight (8n), as 'AABBAABBAABBAABB...' The third column (8n+2) shows a similar but slightly more complex meta-pattern whcih could be described as 'AABBAACCAABBAACC...' Of course, the chart only considers each rule's behaviour when starting from a single 'on' cell, and the pattern may not hold true for other starting conditions. Wolfram also describes a fairly simple hierarchical categorization scheme for the rules, shown below (click for larger view):

Wolfram also suggests that a different, more complex type on cellular automaton (three-state, totalistic), although it has a much larger number of possible rules, still exhibits the same basic patterns. In his words, "Some od the patterns are definitely more complicated than those seen in elementary rules. But at the level of overall behavior, there are no fundamental differences" (A New Kind of Science, p. 65). Most of the chapter consists of descriptios and depictions of various different types of systems, and how patterns created by each type fit into the above categories. The number of different systems and possible patterns seems somewhat unmanageable, but Wolfram suggests that all may be simply categorized as shown above. He concludes, of course, by humbly acknowledging his own brilliance, but he does seem to have created a basic categorical framework that we can use.