I have transcribed quite a few cemeteries and in doing so have discovered what should and shouldn't be put on a grave for planting and decorations.
I've noticed in the last couple of years there is a new fad of putting a shepherds hook beside someones tombstone and hanging various items on it. I've seen humingbird feeders (which I've never seen a humingbird in a cemetery as of yet), hanging baskets, and fancy bird feeders - which both of these do look nice. You also find the small decorative flag poles with a decorative flag.
You also find all kinds of other items laying on or around the tombstones, such as lawn critters, fencing, marble chips, sand. Now using any of the items I have mentioned above is fine and does add a special personal touch to someones grave. But you also have to remember that there are some people who go to cemeteries and do take items off of gravesites, which to me is disrespectful.
As to flowers and plants on graves, that depends on what is planted there. There are some plants that will make a stone more unreadable than others, and then there are some plants that will make the person transcribing or looking for an ancestor in a cemetery not want to go near the grave site.
Yucka plants, also known as Century plants, which are a green long leaf plant with thorns on them will make a tombstone become unreadable after a period of time and also make anyone who wants to see the name on a tombstone think twice before doing so.
Hostas, I have to admit are pretty when they bloom, but unless you are willing to go back to the grave site every year and make sure the plant isn't taking over (so to speak) the stone, this is not a good plant for a grave site cause after a while you can't find the tombstone.
Planting of trees or shrubs, which I have seem small ones planted on the sides of tombstones is a nice touch too, but they should be trimmed back every year so that they don't become so large and hide the stone.
Rhodademdrums, are beautiful when they bloom and look really nice in a yard, but for planting at a tombstone this is not a good idea, especially when this plant increases in size to the point that you can't see the stone.
Rose bushes and berry bushes are also not a good plant to put at a tombstone, because they also grow and take over the stone to where you can't read whos it is.
Peonies, are also beautiful when they are blooming, but these also become large in size and take over a tombstone, not too mention when they are going to bloom there are a million ants running all over them.
Now if you want to plant any of the plants I have mentioned above, consider talking to the caretaker at the cemetery and seeing if they would mind trimming the plant/tree/shrub so that it doesn't become uncontrollable.
The planting of annuals is a nice touch and don't harm the stones or take over to the point that you don't know who's grave you are standing at. Also the use of artifical flowers is nice too, this is what I use cause the grave sites we decorate are not close to where we live and we would not be able to go out and water the flowers when it hasn't rained in several days.
It is best in using real flowers to select small annuals or perrenials. Always remember if it is a perpetual care cemetery check with the caretaker before planting anything. Do not plant things randomly so that in mowing the lot the caretaker is forced to do alot of hand trimming. If a plant/bush is placed close enough to a tombstone to rub across it when the wind blows or there is rain it will eventually destroy the stone.