Paint white to match trim.

And switch brown outlet to white.

They can also be removed to expose the cast iron rads if that look is more desirable.

Paint them.

first you'll need to sand off that glossy finish (or use a deglosser, but you should still do a fine sanding) Prime w/oil base primer, fine sand again, wipe clean, paint.

You could top it w/a diff piece of wood, marble, slate, a cushion, whatever you like. grow some plants on them, put a bed up there for animals.

these look so much nicer.

you can make new ones if you like the wood look, or purchase ready made covers.

this looks great. top w/ a remnant piece of natural stone.

decorative face covers. if you can DIY, the list is endless what you can do

Painting is a good option and these sure look hideous right now. You should paint these.

I think Beth shows some really great ways to make them work in almost every decor

Paint! You will be amazed at the difference in look with a coat of white paint. At my prior house, I painted all the radiator covers to match the trim in the room. Bedrooms and baths were white but public spaces with natural woodwork got a coat of chestnut brown.
Although the cast iron lumps are termed radiators, the majority of heat transfer is actually through convection. Radiator covers do make a difference in the amount of heat in the room. Certain designs are more efficient than a stand alone radiator but most covers restrict air movement. The most important feature is that the cover needs a clear area at the bottom to draw in cool air. Warm air rises and exits through a grill in the top or front of the cover. If you don't like the look of the covers, a simple shelf about 2/3 of the depth of the radiator, mounted about 6 inches above the radiator is a nice look.

Efficiency is lost by covering radiators but if covered, all the more so iif the top of the enclosure is wood.

Even though most thin slabs of stone are not the greatest of heat conductors, they do conduct heat. It's very typical in Europe (where radiator heat is the norm) to have some kind of piece of stone over radiators, whether the front is covered or not. As shown in the fifth picture shown in Beth H's post above. The stone does get warm (hot) and will emit more heat than wood. And will divert the heat a few inches away from the face of a window, for radiators located under one.

I went hunting for radiator covers and found it would cost about $300-$500 for a small one, new, in metal. The quality that I found through the companies I located online was really good, though. They were willing to do custom in any way you wanted. Seemed like family-owned companies that take a lot of pride in their work.

Painting would be a lot more inexpensive. I guess that radiator does not get overly hot, because otherwise a wood cover would have never lasted all these years. If its not a super hot radiator, you would have more choices of paints. If it runs hot, you should probably choose a paint made for that purpose. Generally for paint, I like ECOS - ECOS Radiator Paint