Memoization without array
There are probably better examples, but here is one, off the top of my head:

Let's say you want to check whether the edit distance between two strings $S,T$ is $\le d$, and if it is, compute the edit distance.  You can use the standard dynamic programming algorithm to compute the edit distance, but "prune" the computation (stop the recursion) at any place where the edit distance is known to be $&gt;d$.  This means you probably won't need to fill in the entire table; you'll only need to fill in some of the entries.  Thus, using a dictionary can give a performance boost.