Blue Moon or Hoegaarden Belgian White: Belgian Whites generally go pretty light on the hops, instead relying on orange-peel and coriander as flavoring agents. The grain bill is also light, so you don’t have to worry about bitter roasted malts scaring people away. Blue Moon and Hoegaarden are both pretty innocuous (Hoegaarden is better, but Blue Moon is easier to find), and can help to build up a base from which a novice beer-drinker can spring to more “beery” brews.
Spatin Optimator: Doppelbocks are notoriously balanced towards the malty side of things, and the Optimator is no exception. It is dark and sweet, and there are discernable caramel and toffee flavors, but as a lager it is light enough to not weigh you down. There is hardly any hop bitterness in this beer, which goes a long way towards appealing to those who don’t care for bitter flavors.
Pyramid Apricot Weizen: American Fruit Weizens are great beers for those who don’t like beer. The subtle fruit flavors are often compelling enough to make them want to try more, and weizen yeast ferments with banana and clove flavors, which can be a real draw (assuming, of course, that your target enjoys banana and clove flavors).
These are just a few examples of beers that go easy on the hops and can appeal to those who don’t care for beer. Once someone finds something that they like, you can suggest beers that are similar, but continue expand their tastes. I am firmly confident that there is a beer out there for every taste; you just have to find it.