Is surface-mounted cabling on my basement ceiling a threat to my safety?
Depending on the wire size the NEC expressly forbids stapling to the bottom of the joists, or as the OP has stated fastened to paneling on the bottom of the joists.

From 2014 NEC;


  334.15(C)C) In Unfinished Basements and Crawl Spaces. Where cable is run at angles with joists in unfinished basements and crawl spaces, it shall be permissible to secure cables not smaller than two 6 AWG or three 8 AWG conductors directly to the lower edges of the joists. Smaller cables shall be run either through bored holes in joists or on running boards.


From the OP's post it sounds like they put all the cables in bundles on the paneling. The smaller ones need to be run through the joists or on running boards.

The question would remain if the "paneling" qualifies as a "running board". I would argue that 1by material is needed to qualify as a running board not paneling.

Happy Saturday!