What is the fastest reproducing mammal?

Bandicoots.

Apparently, their gestation period of 12.5 days is the shortest of all the mammals.

http://www.bandicoot-books.com/bandicoot_information.html

There's a reason why they say 'breeding like rabbits'.

"Rabbits have a very rapid reproductive rate. The breeding season for most rabbits lasts 9 months, from February to October. In Australia and New Zealand breeding season is late July to late January. Normal gestation is about 30 days. The average size of the litter varies but is usually between 4 and 12 babies, with larger breeds having larger litters. A kit (baby rabbit) can be weaned at about 4 to 5 weeks of age. This means in one season a single female rabbit can produce as many as 800 children, grandchildren, and great-grandchildren. A doe is ready to breed at about 6 months of age, and a buck at about 7 months."

https://en.wikipedia.org/wiki/Rabbit

According to this site, they can have up to 13 litters a year!

http://wiki.answers.com/Q/How_many_litters_of_rabbits_can_they_have_a_year