Maximum shortest word accepted by pushdown automata
The precise answer depends on your model of PDA (models differ among different authors; compare Sipser to Hopcroft &amp;Ullman).  And number of states alone is not a good measure for PDA's, because there is a well-known tradeoff between states and stack symbols.  For example, a classic construction turns a grammar like

$S \rightarrow X_1 X_1$

$X_1  \rightarrow X_2 X_2$

$X_2 \rightarrow X_3 X_3$ 

...

$X_{n-1} \rightarrow X_n X_n$

$X_n \rightarrow a$

into a 3-state machine accepting the language $\{\,a^{2^n}\,\}$ by final state, no matter how many variables there are, or into a 1-state machine accepting by empty stack.  This gives a classic example of how the shortest string can be exponential in the description size of the PDA.