Varieties: 

There are five main types of carnivorous plants:

Sundews (Drosera spp.): The leaves are covered with sticky hairs which capture and digest insects.

Venus Flytraps (Dionaea muscipula): They have upright traps enclose when touched to trap insects.

Pitcher plants: Insects fall into their tall vase-like tubes. There are five different types: North American (Sarracenia spp.), Tropical (Nepenthes spp.), West Australian (Cephalotus spp.), Sun Pitchers (Heliamphora spp.), and Cobra Lily (Darlingtonia spp.)

Butterworts (Pinguicula spp.): They usually have green leaves that appear glossy but are actually sticky.

Bladderworts (Utricularia spp.): They have incredibly ornamental flowers, and they catch insects with their bladder-like organ roots.

Plant Care*:

Light
Bright, indirect sun, 50% shade.

Watering
Purified water is best. Carnivorous plants love water. Keep them in trays of water so they never dry out.

Soil
Water-retaining soil that's low in nutrients like sphagnum moss. 

Fertilizer
Nepenthes don't need much else besides an occasional insect for food, but if desired, a 1/8 dilution of liquid fertilizer solution can be poured sparingly into their pitchers.

* Standard care recommendations - you may need to adjust based on your home or office environment.