Just curious. If an atomic or hydrogen bomb exploded would there be any components (at all) that could survive the explosion?
A lot of individual nuclei, I guess. And, of course, an equivalent amount of electrons.
The fission in a fission bomb is never 100% right?
No, more like a few %. But the remaining atoms would be completely ionized anyhow.
The temperature of a nuclear explosion can reach 100,000,000 degrees C, more than anything in the immediate area can withstand.
Sure, there will be plenty of fuel atoms left. That’s not what the OP is asking, though. He’s asking whether there will be any solid chunks of the device (fuel, casing, whatever) left.
It seems to me that I’ve seen pictures of a few fragments of metal from the Trinity test, but I can’t remember if they were from the bomb itself, or from the stand it was mounted on.
Would a tiny pellet of plutonium count, even if it had gone through the process of vaporizing - condensing - solidifying?
The only thing left from Trinity was a few twisted stubs from the base of the shot tower. IANA nucular scientist but I’m surprised even that much survived.
As to the OP, most of the atoms in the bomb actually survive. Individually. And not as anything you’d want to see up close.
The fireball in a nuclear detonation is the air being superheated to millions of degrees by ionizing radiation. Any solid component of a bomb is going to absorb far more radiation than air will.
There’s not even an explosive blast wave until after the bomb’s immediate vicinity has been superheated - the blast wave is a result of that superheated material expanding as quickly as it possibly can.
Technically, part of “Little Boy” - the atomic bomb that destroyed Hiroshima - is still around. I’ve seen it.
There was a locking device that had to be removed from the bomb so it would detonate. It was removed in flight before the rest of the bomb was dropped and brought back to Tinian. It’s currently a museum exhibit.
You are probably referring to this fairly famous picture.
ETA: I think that link may not work so here it is explicitly: https://commons.wikimedia.org/wiki/File:Trinity_Test_-_Oppenheimer_and_Groves_at_Ground_Zero_002.jpg
Early in the arms race, the US government was trying every way possible to detect a Soviet Nuclear test. There was a company called Tracer Lab that had expertise in detecting tiny amounts of radioactivity. They suggested equipping planes with filter-paper debris collection systems and flying them in the jet stream. The government scientists were skeptical that this would be useful, but after one of the first US H-bomb tests, the planes not only brought back radioactive particles that Tracer Lab used to pinpoint the time of the explosion, but also tiny metallic spheres, presumably from the vaporized bomb itself.
What were Oppenheimer and Groves doing at Ground Zero after the explosion? Presumably they were at great risk from radiation? What were they thinking?
The description of the photo on the wiki commons says the photo was taken in September, so presumably radiation levels had gone down.
The radiation after-effects from atomic weapons were not well understood then, nor were they predicted to be as dangerous as they turned out to be. This is why if Japan had not surrendered and Operation Downfall, the invasion of the Japanese main islands, had commenced they were planning on using a dozen or so A-bombs along with the overall invasion ground forces.
They did measure the radioactivity at the Trinity site, and it wasn’t deemed lethal. In that pic they are wearing those little booties on their feet at least*!* 
Groves appears to be wearing disposable booties over his shoes (Oppenheimer may be too, hard to see for sure), so maybe the radiation wasn’t completely gone…
And that “button” on Op’s lapel is, I’m pretty sure, a radiation detection gizmo.
Even today people grossly overestimate the long term risk of radiation from nuclear weapons.
Hiroshima today is not a hellish wasteland. It’s a thriving metropolis indistinguishable from any other. As is Nagasaki.
A couple months after an explosion the residual risk isn’t zero, but it’s certainly no obstacle to living there, much less just visiting. Eating the local dirt is not recommended, but it’s also full of worm poop, so you shouldn’t eat it anyhow. 
The mix of radionuclides from a power plant accident, e.g. Chernobyl or Fukushima, is very, very different from the mix from a fission or fusion bomb.
They were truly/generally spheres, not “randomly shaped bits?” Any idea why? I’m thinking of a milk droplet just as it separates and begins descending (nicely enough, in the famous image of Edgerton, which I suppose with Trinity itself makes two for him.)