When wizards die, are their wands recycled? Or are they buried with the wizard or what? I mean, the wand might not be interested in a new master just yet, but it seems like a waste of a perfectly good core and wood.
The wand is generally laid to rest along with its owner. Quoting from Dumbledore’s notes in The Tales of Beedle the Bard:
Most witches and wizards prefer a wand that has “chosen” them to any kind of second-hand wand, precisely because the latter is likely to have learned habits from its previous owner that might not be compatible with the new user’s style of magic. The general practice of burying (or burning) the wand with its owner, once he or she has died, also tends to prevent any individual wand learning from too many masters.
Indeed, this is what happens in one case – Dumbledore’s wand is buried with him. There are very few other accounts of exactly what happened to somebody’s wand after they died.
If the wand is liable to malfunction with a new owner, that might explain why the wood and cores aren’t recycled. (Although I’ve never seen evidence that the wizarding world are particularly conscientious in that regard.)
I’m sure I’ve read something about a wand’s power being “broken” with the death of its master, but I can’t find a reference to it now.
A witch or wizard's wand is usually buried with the first owner, but in some specific cases like Ron, who came from a poorer family, got a second-hand wand, and Neville, who also got his father's wand, was more of a sentimental reason. However, most of the wizards and witches that faced death, were buried with their wands. Dumbledore, Lily and James, and Nymphadora and Remus were buried with their wands. Aside from Dumbledore, I can't find specific evidence to support this, other than Harry would have inherited his parent's wands, and likewise with Teddy Lupin. Most wizards are buried with their wands because, depending on the wood and core types, the wand may "die in power" as quoted from the Pottermore Wand Wood section, and the effects may not be pleasant. There are always special cases but for lack of canonical evidence and examples, I would say that there are always special cases, but mostly they would be buried with their wand.
In the Pottermore section for English Oak, it says,
"It is said that Merlin’s wand was of English oak (though his grave has never been found, so this cannot be proven)."
Which offers proof that Merlin was believed to be buried with his wand.
Besides for Dumbledore's wand covered in alexwlchan's answer, there is another instance in which we are told about someone being laid to rest with his wand. From Chapter Twenty-Two of Half-Blood Prince:
And Odo the hero, they bore him back home
To the pace that he'd known as a lad,
sang Slughorn plaintively.
They laid him to rest with his hat inside out
And his wand snapped in two, which was sad.
It's not entirely clear whether the wand had been snapped specifically for the burial or for some other reason (whether deliberately or accidentally). Though the phrase "which was sad" might indicate that at least the "snapped in two" part waas not considered standard practice.
It depends on the wizard, and the wand.
As mentioned in the other answer, some are buried with their owners.
Some are handed down, but at least in the cases we've seen in the books, this is rarely successful. Both Ron and Neville have more success as wizards not only as they grow older, but when they get their second wand which has chosen them specifically. This may prove different if the match was better, but it seems even brothers and sons using someone else's wand isn't ideal.
The core and wood can make a difference in this matter, as seen on Pottermore. The unicorn hair core description tells us, "They are the most faithful of all wands, and usually remain strongly attached to their first owner, irrespective of whether he or she was an accomplished witch or wizard." It also warns, "they are prone to melancholy if seriously mishandled, meaning that the hair may 'die' and need replacing." Source.
Similarly, the ash wand wood section explains, "The ash wand cleaves to its one true master and ought not to be passed on or gifted from the original owner." Source.
As we can see, some wands may be effectively handed down, most should not be, and some certainly shouldn't be.