As of Volume 4, Episode 3 we have 15 distinct species of Grimm.
They are as follows:
1) Beowolves and Alpha Beowolves
The rank and fodder Grimm
This Grimm seems to be one of the more intelligent species of Grimm and is capable of using other Grimm to its advantage
4) Creeps and an unnamed larger version (Alpha Creeps? Creep Majors? Major Creeps?)
Aside from Deathstalkers, the only species that is confirmed to be subterranean
Aside from Creeps, the only species that is confirmed to be subterranean
6) Dragon/Wyvern Grimm
This is one of the two Grimm which appears to understand human speech. It is also the only Grimm we have seen that can summon other Grimm by directly spawning them to its location
7)Geist (Unclear if this is related to the Possession Grimm from the Manga or the same thing)
This is the only Grimm which appears humanoid in form, as well as possess objects
Note that this is one of the only Grimm we have yet to see fight or be involved in a fight
9) Griffon and possibly Alpha Griffons/Griffon Major/Arch Griffons
10) King Tajitu
The only Grimm which can take two forms. Also the only Grimm to include a reversed colour scheme
Unclear if the smaller versions of Nevermores seen in Volume 2 are baby Nevermores or simply a smaller breed. Note that there is apparently a difference between a Nevermore and a Giant Nevermore, so the larger ones might just simply be nothing more than upscaled Nevermores...unless there is a breed of Nevermore even bigger than the ones we have seen...
12) Sea Dragon/Sea Serpent/Poseidra the Grimmlantean Dragon
This is the only aquatic Grimm we have seen so far
13) Ursa and Ursa Major
Ursa are the only species of Grimm that have a larger named version of themselves. No other species has actually been referred to by RT as an "Alpha" or a "Major"
14) Unnamed insectoid Grimm (The one Cinder summoned)
This is the only Grimm we have seen that has apparently been controlled by a person
15) Unnamed jellyfish-esque Grimm (Which is called a Seer on the wiki but...its on the wiki...so....)
This Grimm can apparently understand speech and communicate long distances between other Grimm. It might be some sort of Grimm mind/overseer/hive mind.
There are still several species which have yet to have Grimm versions:
Any large cat species (A good name for a Grimm Lion would be a Nemean, after the Nemean Lion from Greek Mythology)
A Spider Grimm (For nightmare fuel)
Bat Grimm (Because why not have a swarm of them?)
Deer/Elk Grimm, for fun
Rodent Grimm, because why not
Other bird species (Owls, Hawks, Eagles) Grimm, because they can look different to a Nevermore or be of a different size or something
Lizard Grimm, such as a Komodo Dragon Grimm
An almost endless variety of mythological creatures
Honey Badger Grimm. Because that would be terrifying. And deadly.
I will update this with each new addition. Feel free to post stuff about each species and Grimm and discuss what you want to see more of!