I've had this for years, but never knew the ID for it. Is this one Cylindropuntia acanthocarpa?

Just a wild guess. Texas Tree Cholla Cactus (Cylindropuntia imbricata). My record, I am seldom right. Sorry.
Stush

Thanks, Stush. I looked it up. It looks pretty close except for the flower color. It's definitely orange and not pink.

Hi Karen,

I think you might be right, but it is hard to say with 100% certainty from your picture.
It could also be C. versicolor, which has a variety of flower colors. In this case a careful look at a mature stem (so not one with flowers and vestigial leaves) might help - the spinage and shape of the sections are different. Any chance of a picture of that?

Hello Thijs, thanks for your comment. We travel between 2 places, and right now I'm not with this plant. When we go back I'll get new photos. Meanwhile I'll check the old ones to see if there is a better photo of the stems.