The International Carnivorous Plant Society (ICPS) maintains a list of registered cultivar names for Dionaea muscipula Soland. ex Ellis (aka Venus flytrap).
From Wikipedia: A cultivar is a cultivated plant that has been selected and given a unique name because it has desirable characteristics (decorative or useful) that distinguish it from otherwise similar plants of the same species. When propagated it retains those characteristics.
Here is a complete list of all of the current Venus flytrap (Dionaea) cultivars registered with the ICPS.This list does not include those cultivars which are not fully registered with the ICPS such as Dionaea ‘Clumping Cultivar’, Dionaea ‘ Big Mouth ‘, Dionaea ‘Kinchyaku’, Dionaea ‘Red Rosetted’, Dionaea ‘Royal Red’ etc.
Dionaea ‘Akai Ryu’ – aka Dionaea ‘Red Dragon’
The most common red form of the Venus flytrap. Is known for it’s intense dark red colouration.
Dionea ‘B52′
Currently considered to the largest Venus flytrap cultivar. Optimal growing conditions are required for these plants to reach their full size. Poor growing conditions will result in a plant the same size as any other.
Dionaea Clayton’s Red Sunset
Red with long skinny petioles (particularly during winter) whereas other red cultivars have quite wide petioles. They often lose all of their leaves during dormancy.
Dionaea ‘Cupped Trap’
The traps are joined at one end, creating a cup shape. Despite their warped appearance the traps still function correctly.
Dionaea ‘Dentate Traps’
The spines of each trap are short and triangular like a sharks tooth instead of long and skinny as in ‘regular’ varieties. The spines of small/younger plants do not shows these properties as prominently.
Dionaea ‘Fused Tooth’
The spines of the traps are bent out of shape, fused together by webbing. The traps usually look normal during spring however.1
Dionaea ‘Green Dragon’
This is believed to be a mutation of the ‘Red Dragon’ cultivar, but the edges of the traps do not turn red, even when exposed to intense sunlight.
Dionaea ‘Holland Red’
A red variety which is often green when growing in insufficient light.
Dionaea ‘Jaws’
The traps are very big and have short, pointy spines.
Dionaea ‘Justina Davis’
The traps are always green, even when exposed to intense sunlight.
Dionaea ‘Louchapates’
The spines of the traps are split and found at the ends of the trap lobes.
Dionaea ‘Petite Dragon’
Has the same deep red colour as Dionaea ‘Akai Ryu’ but is not as large and has bifurcated flower stalks.
Dionaea ‘Red Burgundy’
A red variety which is known for having rapid growth characteristics (for a red variety).
Dionaea ‘Red Piranha’
Has short, triangular spines like Dionaea ‘Dentate Traps’ but the intense dark red colouration of Dionaea ‘Red Dragon’.
Dionaea ‘Sawtooth’
Similar to Dionaea ‘Dentate Traps’ but with trap spines which are modified into short, sawtoothed edges.
Dionaea ‘Wacky Traps’
The leaves are incompletely developed. This is an extremely slow grower that also has strangely distorted flowers. Known in some circles as “Bart Simpson”, but this name has not been established and might even violate some trademark laws.
Cultivar Groups
From Wikipedia: Under the botanical nomenclature of the International Code of Nomenclature for Cultivated Plants (ICNCP), a cultivar group is any gathering of cultivars designated by common traits.
Dionaea Dentate Traps Cultivar Group
This cultivar group contains all plants with short, triangular shaped spines.2