Licensed

Licensed pets are pets that are based on an already existing brand, such as Disney or Neopets.
(Technically the Mushiking could have been here, but since it's not as well-known of a property in the US, I have not listed it on this page).

Doraemontchi & Doramitchi

So this technically fits as a Tamagotchi, but as it's not an explicit Tamagotchi shape, I'm listing it.
It functions similarly to a Tamagotchi, but has an inventory and Time Travel features.

The Tamagotchi Wiki has more information.

Tenchi Muyo in Pocket
天地無用! in pocket

Raise the cabbit Ryo-Ohki!

Instructions

G Gundam Pocket

Raise and battle Gundams? I'm not sure, but we do have instructions for this!

Instructions

Keroro24
ケロロ24

Based off of the Sgt Frog anime

Instructions

Thinkway Toy Story

From Disney:
"A galaxy of fun awaits with the Toy Story Virtual Aliens, featuring three aliens to care for: Alien, Alien Bird, and Alien Dog. The CLAW picks out different "alien winners" of a 15-day vacation in Buzz Lightyear's spaceship. Then, it's up to you to feed them, play with them, and make sure they get plenty of fresh air and exercise! Features include lifelike animation, sound effects and silencer, different exercises for each alien, and more. "

Thinkway The Little Mermaid

Assumed to be similar to the Toy Story pet, except with 4 different sea creatures to care for instead of Aliens.

KeroPet
ケロペット


Suki Suki Touch Dr. Slump
すきすきたっち Dr. スランプ


DNYA Mickey Mouse


Virtual Mickey


Pocket Neopets

The Pocket Neopet is the most well-known of the Neopets VPets. Eight different pets were released, with the Bruno and Lupe seemingly being UK exclusives.

The standard Pocket Neopets have the same selection of games, aside from the Bruce and Lupe.

You can name your pet, set the personality, and keep it fed and happy.

Each version came with both a small figure and a card, as well as a code to redeem an item on the Neopets site itself.

The figure is not vital to the device's function, meaning you can fully experience the pet without it.

The games earn you Neopoints which you use to buy food and toys for your pets.

The Aisha comes in both Light Blue and Yellow, the Kacheek comes in both Red and Orange, the Kougra comes in both Green and Yellow, and the Tonu comes in both Yellow and Red. The remaining pets (Bruce, Grundo, Krawk, and Lupe) only have one color option available.

PinkPT has information about most of the games here.

Instruction PDFs on Neopets

Pocket Neopets Deluxe

The deluxe version of the Pocket Neopets added 2 extra pets and 3 extra games to the gameplay.

The figures in these are only slightly more important, as the shape of the pegs at the bottom determine the pet that you are using at the time, but the same can be accomplished by using a stylus or something similar to press the corresponding button size.

Other than the added pets and games, the gameplay is similar, and the games in each device are based off of the location featured on the toy.

PinkPT has information about most of the games here.

Instruction PDFs on Neopets

Neopets Mini Pals

Gameplay is similar to many other VPets, with hunger and happiness to monitor.

There are 5 different games to play and earn Neopoints to buy over 150 different items.

There is an added bonus in this one in that you earn experience and gain levels, with level 50 earning you a code to enter into the Neopets website for an in-game item.

The different pets are:
Red Bruce
Yellow Meerca
Green Acara
Blue Scorchio

Neopets by Zizzle

So... There is very little information on this one.

It seems to work similarly to the other Neopets VPets, just made by a different company.


NeoPens

These were only released in Australia and New Zealand, but there is some information on them!

They are very similar to the Pocket Neopets, except a pen, with some added non-Neopets functions. As well as being a pet, you can store phone numbers, make notes, set a timer, and it even shows special Neopets days in the calendar (well, as of 2004).

Instructions