cardinality of recursive/r.e/not r.e languages?
I assume you're talking about the cardinality of the sets $R$, $RE$, and $\overline{RE}$, as the set of all words in a language is always countable.


$R$ (the family of recursive langauges) is countable, because there the set of Turing Machines is countable, and there is at least one TM for each $R$ language.
$RE$ is countable, by the same logic, since there is a TM semi-deciding each $RE$ language.
The set of non-$RE$ languages, $\overline{RE}$, is not countable, then by process of elimination. The set of all languages, $\mathcal{L}$, over an alphabet $\Sigma$ is $\mathcal{P}(\Sigma^*)$ i.e. the powerset of the set of all words. 
This set is uncountable, since $\Sigma^*$ is countable, and the powerset of a set always has higher cardinality.

$\mathcal{L} = RE \cup \overline{RE}$, and $RE$ and its complement are disjoint, so since $RE$ is a countable subset, there must be an uncountable number of words in $\overline{RE}$.