As a Certified Horticulturist, I've been taking cuttings off pretty much anything that will stand still long enough for me to snip a bit off.
When I first took my training in 1989, I worked for a wholesale nursery in Langley B.C. for the summer, and then went back after the course was finished.
Some of the responsibilities of the Head Propagator (me!) were a bit humdrum, and there was a lot of record keeping to do. I had to fill the schedule and keep tabs on all the plants that were required (making sure I did enough extra to end up with the right number), rooting them, hardening them off, and moving them at the right time to an outdoor bed to finish growing until they were big enough to pot on.
I had a lot of fun learning how to use a mist system, with bottom heat in the benches.
That was a steep learning curve, to get the right amount of mist, at the right timing so that the leaf surface got a small amount of moisture, but no droplets so it wouldn't start rotting.
The bottom heat was supplied by water from a boiler that was circulated in rubber tubes that looped around the benches, and there were miles of the stuff. If air got in the tubes, it would stop the circulation, so I would have to 'bleed' the lines, by leaving a tap open.
In the interim I've worked at a lot of other places, but that was where I got my start, both with the deciduous cuttings of prairie hardy roses, spirea, potentilla and many other shrubs, evergreens like Rhododendrons, Arctostaphylos uva ursi (the nursery sold that by the ton!) and in the winter I took semi ripe cuttings of Junipers and other conifers.
I also did a tiny bit of grafting, with some success, but I couldn't tell you now what was the trick. I did some Acer palmatum varieties that were grafted onto plain old Japanese maple seedlings, and played with some of the harder to root things like some of the Junipers, mostly scopulorum.
The thought was that if they were grafted onto an easy to root form of Juniper, then they would be stuck just like a regular cutting but deep enough that the nurse cutting would root and give the top part enough time to get going that we might figure out a way around that particular difficulty.
The owner of the nursery was always looking for innovative ideas and ways to root difficult plants to produce them more quickly and economically. I devised a system of rooting Daphne cneorum very successfully; if I tell you, I'll have to kill you, as it's a very secret technique. Espionage is rampant in the nursery industry - I'll bet you didn't know that!
Now I just concentrate on hardy succulents like Sedum, Sempervivum, Jovibarba, Orostachys and Rosularia. They don't require as much fiddling with getting the exact right temperature and conditions; in fact, many of them root without soil at all!