Our house has vinyl siding. The cable company routed the cable horizonally half-way up the side of the house and just left it hanging. Is there some kind of attaching clip I can use to attach the cable to the side of the house without putting holes in the siding? Maybe some kind of clip that slips under the the siding and holds the cable secure? Thanks for any suggestions.

I do a lot of siding and I've never seen a clip that does not require a hole in the siding.
If it's at a corner the cable can be tucked in behind the outside corner bead.
Your lucky, I've seen then cut thru screens, lay the cable on top of a deck instead of going under it, install the cable on top of a window sill so the window could not be closed, and the best one was cutting the screen and pulling the cable so tight in front of a bathroom door and running it over a set of steps (not under it)that the door could not be opened. All because they were to lazy to go under the house.

This may be just me being ignorant, but have you called the cable company to let them know? This was probably a contractor they hired to do the installs, and I'm sure they would rather you be reasonably satisfied with the job instead of cancelling service...(that's always my threat.

Our local cable guy tried something similar for me...but it was with the phone box...he installed it about (my) head level right where I had to roll my trash cans on a narrow walkway...first time I tried it, I knocked my head on it, and they were out the next day to replace it.