Earth has a human population of over 7 billion, and I doubt there are any larger animals in numbers even approaching that, since many of them are threatened or endangered. What is the next largest animal to humans that outnumbers humans? There must be something between humans and insects.
I would imagine chickens greatly out number humans. Possibly rats.
Here’s an article that tries to address your question. The consensus is the brown rat, but they also conclude its really hard to estimate.
I heard, somewhere, that the average human being has about ten times as many bacterial cells in his body as human cells. Bacteria, of course, are very small, and very numerous. I’m sure that they outnumber humans at least by a factor of millions, if not more.
Here’s a link to a picture of some bacteria that I scraped from my teeth a few years ago: Several different types of bacteria appear in this picture. The larger red objects are probably some of my own epithelial cells. I took this picture using my 15× eyepiece and 100× oil-immersion objective. The numbered scale that you see is built into this eyepiece, and when used with this objective, the numbered ticks are eleven (11) microns apart; a micron being 1/1000 of a millimeter, or 1/1,000,000 of a meter.
No cite available, but I’ve heard that there is a ton and a half of termites for every man, woman and child alive. Considering their modest individual weight, I’d say that’s a lot of termites.
Chickens - the world chicken population is something like 3 per person, and this indicates that it is the only livestock animal which outnumbers humans:
I really doubt that any wild animal larger than a chicken beats that, particularly if we don’t lump any similar species together.
According to this source, there are around 19,000,000,000 chickens in the world. Cattle are the second most populous domestic animal at around 1,400,000,000 and there are around a 1,000,000,000 each of pigs and sheep. I also found another site which said there are 900,000,000 goats in the world and their number is rising so they may soon break the billion mark. Buffalo are leveling out at around 200,000,000. And the number of horses in the world was somewhat implausibly given as 58,372,106 in 2006.
So chickens have us outnumbered but we’re still ahead of the large mammals.
There are plenty of fish in the sea, probably more of some species than of anything (in the relevant size range) on land, jellyfish too, and other invertebrates.
From the NPR article, among species Antarctic krill (Euphausia suberba) is the reigning champion with a population of 500 trillion. They can grow to a length of 6 centimeters.
Hardly a fair comparison, though, since you’re comparing an entire superkingdom of life with a single species.
Birds, fish, small mammals, insects, reptiles, amphibians - there are plenty of species that number more than 7 billion. I wouldn’t be surprised if there are more than 7 billion sheep or goats, either.
Got any examples?
Trying not to hijack too much, but to correct for size, are there any animal species that out-mass humans? Chickens do not, certainly, if they only outnumber us 3-1.
NEMATODES! 
We did this not too long ago in another thread. I looked, but couldn’t find it.
I’d suggest cattle, if there really are 1.4 billion cows as cited above.
The average cow is something like 400kg which would be 560,000,000,000kg.
If the average human is a 75k (and I have to think that is high due to children and most of the world not being American) that would be 525,000,000,000kg.
I’m sure ants, for example, outmass, but I don’t know if any individual species of ant does.
Per the link above, Euphausia superba is thought to have a total biomass of 500 million tonnes, compared to 350 million tonnes for Homo sapiens.
For some reason I find the thought of 350 million tonnes of human flesh rather horrifying.
Edit: and as obfusciatrist says, cows have us beat too - and at about 520m tonnes they probably even push the krill into second place in the single-species ranking. That link also says that the accepted average for humans is 50kg, to take into account children and non-supersized adults.
I heard we have the highest number of heart beats in an average life span than other animals. I define animals in my mind in such a way that mean warm blooded. So using that criteria, total number of heart beats, what warm blooded mammal / animal has the longest life time in # of heart beats?
Also, leaving out chickens or anything smaller than a human, as requested in the OP, what has higher numbers?
fair enough, but I am sure that even if you get down to one common species of bacteria, it will still outnumber us by a similar factor.
The picture that I posted is from a very small sample, scraped from my teeth, and spread on a microscope slide. Of that sample, this is a tiny portion of that, that fits into the area covered by this image, which is a square that is 60.8 microns on a side (that’s 0.0608 of a millimeter). I’m sure that there are hundreds—perhaps thousands—of individual bacteria visible in this picture, and there aren’t nearly that many different types. Of any one species of bacteria that appear in that picture, there are surely hundreds of individuals. And of any one species of bacteria shown in this image, there are probably millions—perhaps billions—of times as many remaining in my body. I suppose it is probably safe to say that there are probably several unique species of bacteria such that the typical population of these bacteria on one average human body far exceeds the human population of the world.