The most commonly recognized is the Shaker, with clean, simple, classic lines that many designers feel will never go out of style. Each door has a frame at the top and bottom, as well as on the sides. The center panel can either be raised or recessed and will fit into any decor.
Glass-front cupboards have a reflective quality that can brighten a dark room, especially when twinkling lights are added to inside doors.
Beadboards have vertical slats that fit into each other. The boards or planks can vary in width, making it more textured. Since one of the characteristics of cottage decor is texture, this can fit in nicely.
The flat-fronth as no panels or framing, it is very minimalist and even stark but works well in modern kitchens.
The last two give a warm, rustic and organic look that's so popular right now: plywood and natural wood; just be sure the latter has a kitchen that's well vented so humidity doesn't build up.