I believe that "balsa cement" was a name used by some model sellers to avoid infringing the ®Duco tradename. This is basically just polystyrene/polyethylene plastic dissolved in acetone.
It has largely disappeared from the market partly because it's been used by kids "glue sniffing." The actone solvent does produce a sort of "high" and in even slightly concentrated doses can cause substantial brain and nervous system damage. I've met a couple of lovely young zombies who experimented. Their remaining "personalities" approximated that of a clothing store mannequin (that requires constant attention with toilet and eating functions).
It's also not useful for the new plastic models, which are mostly made of polyvinyl or polypropylene, or even nylon, and the acetone solvent won't react sufficiently for that kind of glue to stick. The newer pvc model glues are somewhat less toxic, they work (sort of) on some plastics, they don't scare mother and the local cops, and they don't destroy kids.
You probably can still find the same basic product under the brand name "Duco" at some hardware stores, craft shops, and model shops. Properly used it's safe enough.
At the lumber yard, you can get much the same basic product as the newer PVC model glue as "pipe dope" for gluing together plastic plumbing. The "PVC" grade is generically similar to - not exactly like - the PVC model glue, dries clear, and is used for white plastic pipe. It's a fairly good glue for light wood/paper assembly, although it's not packaged for easy use in small quantities. I'd recommend buying the stuff in the tube or small bottle at the model shop, hardware, or art supply store for most uses.
The "ABS" grade dries black, and is used on black plastic (ABS) sewer pipe. For small jobs, I'd still recommend going to a model, hardware, or art supply store. The ABS grade pipe dope also makes a pretty good glue for auto body and trim parts that happen to be made from ABS plastics, although some filler or reinforcement may be needed. Since this kind of repair often requires fairly large amounts of glop, the ABS pipe dope is not too bad a way to get it if large quantities are needed.