Kalanchoe daigremontiana I believe.

A few Kalanchoes (a type of succulent) have a very different way of producing the next generation of plants. Little plantlets grow all around the edges of the leaves. (It has nothing to do with the leaf rotting; they will grow on the living leaves also.)

The kalanchoes which do this are usually nicknamed "Mother of Thousands" or "Mother of Millions."

They can be a real nuisance in a warm climate.

Photos here of a mother plant with leaves full of plantlets:
http://www.worldofsucculents.com/kalanchoe-daigremontiana-mother-of-thousands-alligator-plant-devils-backbone/

This post was edited by missingtheobvious on Fri, Nov 8, 13 at 18:45

A friend that was moving gave me one of these, I didn't want it but took it not wanting to offend. It is the biggest nuisance plant! I put it in the atrium till I could get rid of it. In the short time it was there it spread babies every where, they are even growing up between the tiles. I would caution about the abundance of reproduction of it!

Kalanchoe pinnata

These all grow babies on the leaves (and there may be others):

Kalanchoe daigremontiana
Kalanchoe delagoensis
Kalanchoe x houghtonii
Kalanchoe laetivirens
Kalanchoe pinnata
Kalanchoe tubiflora

Kalanchoe 'Pink Butterflies' is a hybrid which makes pink plantlets, but since they lack chlorophyll, they reportedly don't turn into new plants.

As revencajun says, a TERRIBLE plant. Many years ago I had one in my greenhouse in England and I swore that the plantlets had legs as they very quickly appeared everywhere, meters from the parent.
Here in Oz, both K. daigremontiana and K. tubifolia are both feral weeds with have taken over large areas.
Being succulents they have a waxy cuticle and even Ken, with his propensity to spray with RoundUp, would, I suspect, put them into the "Most evil Plants in the Universe" category. :-)

K. daigremontiana has naturalized in Florida, Hawaii, and Puerto Rico.

K. delagoensis is in those states as well as Texas.

K. pinnata is in Florida, Puerto Rico, and the U.S. Virgin Islands.

And K. gastonis-bonnieri (which must be added to the list of those which grow plantlets on their leaves) is in Florida.

And K. beauverdii (which must also be added to the list of kalanchoes which grow plantlets on their leaves) is in Hawaii.

Apparently none of the other kalanchoes which spread in that manner have naturalized in the U.S. yet. However, these other kalanchoes have also naturalized:

K. blossfeldiana: Florida and Puerto Rico.

K. fedtshenkoi: Florida, Hawaii, and Puerto Rico.

K. integra: Florida, Puerto Rico, U.S. Virgin Islands.

K. laciniata: Florida.

http://plants.usda.gov/core/profile?symbol=KALAN