species identification - Can an organism exist as a single cell but come together as multi-cellular during certain times?

I am trying to remember a particular segment from a BBC special, about a single celled species. However, at certain times all the individual cells came together to form a structure, not unlike a mushroom, to scatter something like spores into the wind. Afterward, the individual cells separated and continued on as individuals.

Am I remembering this incorrectly? Is this even possible?

Answer

Welcome to Biology StackExchange.

Am I remembering this incorrectly?

No, you're remembering it correctly.

I think you're talking about slime molds. You'll find more information on the wiki page

Is this the video you saw? These images are pretty cool.

Is this even possible?

Yes (given that it exists). There is no way to correctly answer this question as it really is an open-ended question. But here are a few words that may push you writing further posts.

Just a few words on the evolution of altruism

The main interest behind this life-cycle is that not all individuals reproduce. Some individuals form the stalk while others go through meiosis (see below on the life-cycle).

How unfair does it seem to those who form the stalk! Why would those individuals forming the stalk spend energy to help other individuals to reproduce?

Kin selection

Let's think about us, vertebrates, "real multicellular" organisms. The cell that is in your eye is never going to reproduce. Although it is spending all its energy into helping your ovules/spermatozoids to fuse. Why would this cell in the eye make such an effort? The genes in the spermatozoids/ovules are essentially the same as those in the "eye cell". Therefore, by helping your spermatozoids/ovules the eye cell is actually contributing to spreading copies of the genes that it is carrying. This is referred to as kin selection.

Slime molds and altruism

Now, the story is not exactly the same for the slime molds. The cells in the stalk can be quite different from those that are undergoing meiosis. Altruism can exist in a variety of different mechanisms and it would take several books to go over the literature about the evolution of altruism. Without knowing the literature specific to the slime molds reproduction, I just want to notice that the cell in the stalk will die anyway, whether or not it spend energy helping other cells reproducing. There is, therefore, no fitness cost into construction a stalk. Little population structure (causing higher relatedness within deme than among demes) could be enough to allow this behaviour to evolve.

Just a paper (that I haven't read) on the subject

Hudson et al. 2002

Genetics of the fruiting body

Interestingly, similar genes are being used in Dictyostelium discoideum (slime mold) to create this fruiting body than what is used in multicellular eukaryotes (ref.). Thanks to @Tim Cutts for this info.