The most common dill pairing is with seafood (particularly salmon), and it plays a major role in the flavor of traditional gravlax salmon. However, dill also works very well with a wide variety of produce, including beets, carrots, cucumbers, cabbage, cauliflower, and beans.
More unusual dill pairings include eggs, veal, bell peppers, crayfish, and lamb.
Use fresh dill to brighten up veggie dips (particularly dips based on sour cream) or stir some in to tuna or potato salads. It can be used to flavor pickling brines, but will impart a different flavor to the finished pickles than is found in most store bought varieties.