Why do liquids separate in space with no gravity?

Because liquids, water in particular have a high surface tension.

For this reason blobs of water tend to become spherical. Now, given that it starts as an elongated stream (say because it's pushed out of a bottle), the stream breaks up in different pseudo-spherical bubbles; if an astronaut were to pour water very, very slowly and carefully he could create a single spherical blob.

The concept is not dissimilar to drops, but without the gravity.

A cylindrical column of a liquid is intrinsically unstable due to surface tension. This is called the Plateau-Rayleigh instability. Check out this pdf for some pictures and equations. When you squeeze a liquid out of a bottle, it initially has a somewhat elongated shape, and the instability develops.

Consider a spherical drop of liquid floating weightlessly. Now apply some mechanical energy unevenly to it. You have the mechanical energy of internal fluid flows competing against surface tension, which seeks to restore it to the lowest energy spherical state. But surface tension if not all that strong, if the internal energies within the drop are too large, they can cause it to break into two of more droplets. The real key to getting large drops, is to launch it with minimal internal (fliud) energy.