I LOVE them but it depends on the dish....
I do an Italian tuna salad with the olive oil packed tuna which is a very strong tuna flavor and the capers still stand strong in the total flavor.
I put them in a couple of red sauces I make. Definitely in some salads and dressings and condiments such as tartar sauce.
Of course I use them in picata sauce both a basic traditional and other variations like cream based picata or picata with mushrooms and serve over veal, chicken and even fish.
I think they go good with chicken, pork, veal and fish dishes and some shellfish.
I think they work best in sauces like butter/wine sauces but also do pretty good in cream sauces. They don't jump out at you in the red sauces but add a definite piquantness to them that I like.
I think that a good rule of thumb is that where you think olives do good, particularly green olives, capers work well with also. And they also work well where acids work well such as paired with lemon and even with dill.
They are good just 'fried' in butter or olive oil and then poured over meats or pasta with the oil as a sauce.