How can I realize "sticky" collision, i.e. that objects connect as soon as they touch? I'm fairly new to Blender (great piece of software btw), so please bare with me.

I'd like to have multiple spheres (up to 50), which move randomly in space and as soon as two spheres collide they should stick to each other and move on together.

How would you approach that problem? I already tried to make the spheres rigid bodies and set the friction parameters insanely high, but it did not work. I also tried to use lennard-jones force fields (I also cranked up the strength fairly high), but that did not work either.
Try the free molecular script Add-on. here is a tutorial on how to use it:
https://www.youtube.com/watch?v=haS3B6q82kY