With dairy-based desserts such as Ice Cream, flavors are still more useful to keep in mind than the dessert itself. After all, we can all list about 1001 different types of ice cream that vary quite a bit.
Keeping flavors in mind, the rule of thumb is this: for deep, powerful flavors like Chocolate, you need a deep, powerful wine. Try pairing chocolate ice cream with a Red Burgundy.
For more fruity desserts, pair them with lighter, fruitier wines like Viognier or Chablis.