Made of material that was first developed by NASA in the 1960s, memory foam pillows are made out of specially treated polyurethane that is designed to retain its initial shape after a night of use. As you can guess, the major advantage of memory foam pillows is that they're extremely supportive, which makes them a good option for people with back or neck problems. SleepLikeTheDead.com says memory foam pillows are an especially good choice for side sleepers, who "like how the pillow does not cause their nose to sink into it as is often the case with fibrous and down pillows."
One aspect of memory foam pillows that may take some getting used to is their sensitivity to temperature, which is what gives them their "contouring" properties: They're firmer when cold and less firm when warm. The problem is that these pillows don't breathe, meaning they retain body heat, and we've read some reports that they sleep "hotter" than natural cotton or down pillows. Another issue is what experts call "off-gassing," the tendency of new memory foam pillows to emit an unpleasant, chemical odor that can persist for days or weeks. Also, memory foam pillows tend to lose their ability to retain their shape after months or years of use, though some brands are seem more reliable than others. The most well known brand is Tempur-Pedic, but you can find less expensive memory foam pillows at big-box stores.
Memory foam pillows are more resistant to dust mites than other varieties because, as SleepLikeTheDead.com points out, "dust mites tend not to like to eat memory foam." Otherwise, experts say, memory foam pillows are hypoallergenic and anti-microbial.