There are several types of Zanpakutō, classed by the main purpose or effect of their special abilities. These types include:

Melee-Type Zanpakutō: Are typically designed for various forms of armed melee combat rather than magic-based abilities.
Ichigo Kurosaki / Hollow Ichigo
Kenpachi Zaraki
Renji Abarai
Ikkaku Madarame
Makoto Kifune
Shuhei Hisagi
Marechiyo Omaeda
Sajin Komamura

Kidō-Type Zanpakutō: Are designed around a special ability rather than close combat potential.
Yumichika Ayasegawa
Momo Hinamori
Sōsuke Aizen originally claims his is a "flowing-water-type Zanpakutō," but this is later proven to be a lie.
Retsu Unohana
Kisuke Urahara
Kaname Tōsen
Hanatarō Yamada

Projectile-Type Zanpakutō: When released separate into many air based blades/or substance-based projectile that the owner can control freely.
Jirōbō Ikkanzaka
Byakuya Kuchiki
Rangiku Matsumoto

Defense-Type Zanpakutō: Are designed around defensive capability with little or no offense.
Rusaburō Enkōgawa

A large amount of the Zanpakutō are classified by elements, generally utilizing their respective elements as forms of attack. (It could be said that elemental Zanpakutō are all Kidō-Type which have an element based as noted by Kenpachi Zaraki and Maki Ichinose during their battle, but as this was only mentioned in the anime Episode 98 it cannot be stated as fact.)

Fire-Type Zanpakutō: Designed to manipulate fire for various forms of attack or defense.
Shigekuni Yamamoto-Genryūsai
Shūsuke Amagai

Ice-Type Zanpakutō: Designed to manipulate ice for various forms of attack or defense.
Tōshirō Hitsugaya / Sōjirō Kusaka
Rukia Kuchiki

Earth-Type Zanpakutō: Designed to manipulate the ground for various forms of attack or defense.
Zennosuke Kurumadani

Wind-Type Zanpakutō: Designed to manipulate wind for various forms of attack or defense.
Shunsui Kyōraku
Kensei Muguruma
Senna

Water-Type Zanpakutō: Designed to manipulate water (& related effects) for various forms of attack or defense.
Kaien Shiba / Aaroniero Arruruerie (taken from Kaien Shiba)
Jūshirō Ukitake

Plant-Type Zanpakutō: Designed for the manipulation of plant growth for offense or defense.
Ryūsei Kenzaki

Light-Type Zanpakutō: Designed to manipulate light for various effects.
Maki Ichinose

Poison-Type Zanpakutō: Designed to administer poison as a form of attack.
Soifon
Mayuri Kurotsuchi

Electricity-Type Zanpakutō: Designed for manipulation of lightning for offense or defense.
Seigen Suzunami

Unknown Types (These are the Zanpakutō that while the names and shikai are known, their type cannot be readily verified.)

Gin Ichimaru
Izuru Kira
Chōjirō Sasakibe
Isane Kotetsu

Sub-TypesThere are a few "sub-types" of Zanpakutō classification such as:

Constant-Release Type: Zanpakutō that are always in shikai form because of the strength of their wielder's spiritual energy.[11]
Kenpachi Zaraki
Ichigo Kurosaki

Dual Bladed ZanpakutōDual-Blade Type: Zanpakutō that feature more then one blade in Shikai release. It is decidedly rare for one to possess such a weapon and therefore it says a lot about the uniqueness of its wielder's spiritual power.
Jūshirō Ukitake
Shunsui Kyōraku
Shūhei Hisagi