I was just thinking about this, as I noticed most of my vals have runners/baby plants poking up next to the big plants (which is awesome btw). Will my other plants reproduce like this, or is it only certain kinds?
No, as said above, rooted plants usually do. However sword plants will get stalks where baby plants will grow or the stalk will just flower, both of which are a great sight. So, stem, rhizome, mosses, don't.
Crypts do, but usually it is still connected to the main root, it just depends how far that goes usually.