Up until last year, I've used foil-coated foam board for tombstones. To be honest, I've never been satisfied with it. It's too fragile for my purposes, it doesn't stay solidly rooted in the ground, and after storage in the summer heat it curls up into something that looks like a giant Frito. So I set off on a search for a better way.
What it yielded was contractor's cement board. This is used the same way as drywall in places where water resistance is required, such as areas behind showers and baths. I use a brand called Hardibacker.
It is rock solid and shrugs off wind and rain. It retains its shape and color indefinitely. It is stupidly simple to mount if you have a square nose shovel and a plot of earth. If it breaks, you can patch it with some liquid nails and it will be as good as or better than new.
There are disadvantages though. It is expensive; a sheet(I can't remember exact dimensions) will produce two "standard" size tombstones, a skinny one, and some useful miscellaneous pieces, for about ten dollars, which is still a super bargain over store-bought stones. It is two-dimensional; a quarter to a half inch in thickness. This means you have very little wiggle room for engraving. While we're on the subject, cutting and carving can be quite difficult without the proper tools, because this stuff is HARD.
If you decide to give it a try, make sure you have a circular saw(turn the blade backwards to the the "slopes" of the teeth hit the material first, or get a special concrete blade), a jigsaw for detail cuts(no good way to save the blades, just buy lots) and a dremel tool with several different bits for engraving.
This is the best material I've found short of four-inch granite, and all my tombstones are now concrete board. I'll post pics as soon as I work up the gumption to upload them.