Hypoallergenic formulas are occasionally recommended by pediatricians for babies who have a severe problem digesting cow's milk based formula or soy formula. Hypoallergenic formula, also known as elemental formula, has been pre-digested to be broken down into smaller proteins. This process makes the formula less likely to cause allergic reactions. However, the refinement throws off the nutritional balance as compared to breastmilk and other infant formulas, not to mention means it is much more expensive. For those reasons, hypoallergenic formulas should only be used when a doctor recommends it in light of clear medical concerns.
This type of formula can come ready-made or in powder that you would need to mix with water. See also: Water Guidelines for Baby Formula.
What about generics, DHA, and the like? For more info see: