Ta da!!! Here is a short list that may not be complete, but at least provides
some assistance in your search and some useful search terms (e.g., eutelic).

If your C. Elegans example is a valid instance of counting, then Tardigrades
would also be. Tardigrades always have the same number of cells, usually
around 40,000. No one has ever actually counted the exact number. However, it
seems that counting the number of cells in small organisms is pretty easy
today, just search for this type of equipment on google.

Search Terms:
MUST: Organisms
EXACT: "exactly the same number"
1 OF: quills feathers eyelashes cells eggs fungi sperm flagella
NOT: chromosomes chromosome

Other search terms: Eutelic, determined, model organism
e.g., "animals that lay a determined number of eggs"


1.0 Cell-oriented Creatures

Protista asexual daughter colony formation
Property: One or more cells leave the algae colony and form an exact copy of
the original colony with exactly the same number of cells.
Mechanism: Daughter colony is completely formed before it can escape,
therefore, binary cell division.
Occurrence Rate: Rare
Type of counting: # of cells in the daughter colony is precisely the same as
the number of cells in the parent colony, even though perhaps only one cell
leaves the parent colony to form the daughter colony.
Type of counting: Not really counting, more likely just cell division.

Eudorina colony size
Property: All colonies are 32, 64, or 128 cells.
Mechanism: Probably binary subdivision with communication or detection.
Occurrence Rate: ?
Type of counting:
Type of counting: Variable, but more than just a trivial power of two that
could be explained (in some ways) by binary mathematics of cell division.

Any Eutelic Metazoan, such as a Rotifer (phylum Rotifera)
Property: Eutelic. All creatures of the same species have the same number of
Mechanism: Probably binary cell division with termination point.

Dicyemids: Mesozoans (which makes them halfway between Metazoans and
Property: Eutelic. All members of the same Dicyemid species have exactly the
same number of cells.

Property: Eutelic
Type of counting: ~40,000 cells (apparently no one has bothered to count each
one. BUT! You could probably do it yourself nowadays).
Reference: http://www.earthlife.net/inverts/tardigrada.html
Search terms: cell counting (on google, you will get lots of ads)

Quote from this page:
"Tardigrades are what is called eutelic, meaning there is a fixed number of
cells in the body of an adult of any given species, this is normally around
40,000 cells. Tardigrades have 8 legs, but these legs are not jointed like the
legs of insects and spiders etc. They have a relatively large brain and a well
developed nervous system with a double suboesophagal ganglia and 4 further
ganglia along the body."

Eutelic organs
Property: Even though an entire organism is not eutelic, sometimes specific
organs are.
The eutelic nematode Ascaris always has 162 neurons.

1.1 (Potentially) useful papers

Here's an interesting paper on how cell counts of 959 (and other values)
might be occurring.

Some interesting data on something called pseudocoels, of which C Elegans is
an example. Page doesn't allow "Find" in I.E., but maybe there are some
useful search terms. C Elegans always have 80 cells of pharynx.

1.2 Low-level (sub-cellular, e.g., chromosomes):

Aulacantha (Protozoa)
Property: All have 1600 chromosomes
Mechanism: Chemical reaction
Type of counting: N/A

Polyploidic Endoreplication in Plants
Property: Ploidy is the number of copies of chromosomes in one cell of a
species. Humans have ploidy of 2. Various algae and other cellular creatures
have unusual ploidy counts. Some salamanders have ploidy count of 55. Sugar
cane seems to have the largest number of chromosomes, with 80.
Mechanism: (Guessing) Cell chromosome duplication system that relies on
exhaustible resources within the cell wall during cell division?

1.2 Multi-species creatures and inter-related species

There is something on genetic heredity, where only a certain number of
symbiotes are able to be within a host animal.