Asian Baby Carriers :  There are three main types of these, Mei Tais (MTs), which are based on a traditional Chinese carrier ; Onbuhimos (onbus), which are Japanese; and Podaegis (also spelled podegi), which are Korean.  They all are basically a rectangle with long shoulder straps.  Mei tais also have waist straps.  Onbus have rings at the waist through which you thread the shoulder straps, and podeagi straps are just twisted or crossed under the baby 's butt and then tied around your waist.
Soft Structured Carriers : Similar in construction to mei tais, but with buckles and a structured waist/hip belt.  Some find them easier to get the baby on your back; can offer more support to your lower back as well.   The Ergo is probably the most well known SSC.
Ring Slings : Basically a long rectangle of fabric that's threaded through two rings, so it's extremely adjustable.  Especially handy for before your post-baby weight has stabilized or if you're going to share the carrier with someone else.  Some people say it has a steeper learning curve than other carriers, but others get the hang of them right away.   There's a "tail" of fabric that hangs down, which is especially popular with breastfeeders, as it can be used as a built-in cover up.  Unpadded slings fold up pretty small, so you can even have one as a back-up in your diaper bag.  There are a couple of different shoulder types, including gathered, pleated, and hot-dog, which affect how it cups your shoulder.
Pouches :  A pouch is similar to a ring sling, except that it's sized, and has a seam that creates a pouch for the baby to sit in.  Non-adjustable pouches do not have the tail.  These are really handy for quick trips to the post office or when you're not going to wear the baby for that long (when they're heavier).  They're often easier to get the hang of than ring slings, but can be harder to get the correct size.  Since they use less fabric, they fold up even smaller.  There are a few vendors who make adjustable pouches, with or without a tail.  These are especially useful while you're still losing baby weight, or if you want to share with your husband, grandma, etc.
Wraps : These are basically long pieces of cloth that you can tie in a ridiculous number of ways. Stretchy wraps (like the Moby) are fantastic for newborns and younger babies, while woven wraps are more supportive for heavier babies.