Is it our own species?
It’s gotta be some rodent - mice or rats.
Either of the above is a good guess. It might also be one of the things that we domesticate, like sheep or cows. But I’d probably go with us, if you’re limiting it to one particular species - the world rodent population is made up of bunches of different species. If we’re looking at some higher level taxonomical group, then probably some subgroup of rodents wins, because the primates don’t add that much population to ours.
It’s a close-run thing. My first thought was that it was definitely humans, with rats coming second. A google search for “world rat population” brought up a page with this snippet:
http://www.ucg.org/articles/gn16/Diseases.html
So, if you believe this site, the results are:
humans 6x10^9
rats c.4x10^9
mice >=4x10^9
so the OP’s guess is right.
Note also that the quoted rat population includes more than one species of rat.
As a general rule, the smaller an animal is, the more common it will be. So I would first suspect shrews, moles, voles, and mice (with rats, bats, and squirrels next). But most of those are divided among many different species. For example, the Encyclopedia Americana says shrews are the commonest mammal in the Eastern U.S., but there are over a dozen different species in North America. There are estimated to be 10 billion bats in the world, but again, divided among many species.
Taking a closer look at the most widely distributed species of mammals, we find they are all associated with man. The house mouse (Mus Musculus) is found worldwide, the Norway rat (Rattus Norvegicus)is found throught the temperate zone, and the black rat (R. rattus) is found throughout the tropical zone. Domesticated mammals are widely distributed but it doesn’t appear that any of them is more common than man. Poultry comes close in numbers, but of course they aren’t mammals.
I suspect the rodent population estimates given above are underestimates. During population explosions, the rat population has been measured at up to 1,000 per acre and the mouse population at up to 80,000 per acre (that’s per acre, not square mile). These are extremes, of course, and not averages (and not sustainable either), but they compare to less than 40 people per acre in New York City.
There was a similar question on one of the quiz shows recently, and the answer they gave was that the mouse was the commonest animal in the United States. You can’t always believe the quiz shows, though. I found the claim repeated many places on the Internet, but without a good cite. If it’s true, I suspect there might be even more mice relative to the human population in countries with less of an emphasis on hygiene.
In any case, if the answer isn’t people, we must be pretty close to the top of the list.
Just give us another 50 years. 
My guess would be bats, counting all species.
If you’ve ever seen a flock of bats leave a cave, then realize there are probably thousands of other cave like that, that’d be your answer too.
I don’t think they have natural predators, since living on the roof is a pretty safe arrangement.
IIRC, half of the 4000+ species of mammals are bats, so that’s another factor multiplying their total.
Humans smoke more marijuana than all other species combined, therefore we most definitely have the “highest” population.
I’d be likely to guess some form of rat, mouse, or shrew, but I don’t have any cites handy so I don’t know if hibernicus’ estimates are underestimates or not.
I’d think that it’s probably not bats… number of species doesn’t necessarily indicate overall abundance of individuals, and there are more species of rodents (about 1,700) than there are of bats (about 850) anyway.
If that were the question, I’d probably go with Nematodes.
You ever see the mouse plague on the Crocodile Hunter? Looked like there might be more of them in those few fields then the entire continent of Australia. I bet mice and rats population graphs have a lot of spikes and valleys and may on occasion pass us by for a few months.
Coming from you, my brother, I’ll take your word for it.
It’s a long story how I came by this information, but this is from the 1999 Guiness Book:
“The number of rats in the world today is roughly equal to the number of humans (about 5.3 billion), but will increase more rapidly in the future. One 1993 British survey estimates that rat infestations in large towns have increased by 43% in the last 20 years!”
Of course, this doesn’t make the rat the most populous mammal, but it does put them in competition with us.