Does the Taboo jinx work while in Hogsmeade and/or Hogwarts? Or would it be rendered useless? I can't remember, and I've lost my copy of Deathly Hallows. Any knowledge would be appreciated.
In theory, it should be possible for the Taboo Curse to work both in Hogsmeade and at Hogwarts because the Taboo breaks all protective enchantments. The exception seems to be No. twelve Grimmauld Place.
Once Ron reunites with Harry and Hermione after their fight when Ron left, Ron tells Hermione and Harry how the Taboo Curse works:
‘Sorry,’ said Ron, wrenching Harry back out of the brambles, ‘but the name’s been jinxed, Harry, that’s how they track people! Using his name breaks protective enchantments, it causes some kind of magical disturbance – it’s how they found us in Tottenham Court Road!’
‘Because we used his name?’
‘Exactly! You’ve got to give them credit, it makes sense. It was only people who were serious about standing up to him, like Dumbledore, who ever dared use it. Now they’ve put a Taboo on it, anyone who says it is trackable – quick and easy way to find Order members! They nearly got Kingsley –’
Deathly Hallows - page 316 - Bloomsbury - chapter 20, Xenophilius Lovegood
It's not exactly clear why Grimmauld Place remained safe from Voldemort, because the trip was using Voldemort's name often and openly. Perhaps the enchantments that allowed Grimmauld Place to remain hidden were exceptionally strong. On the other hand, perhaps the Taboo did work, because eventually, after the trio said Voldemort's name, Death Eaters appeared on Grimmauld Place and seemed to be patrolling the space where No. twelve should be, and in order to Apparate to or from Grimmauld, the person Apparating or Disapparating had to hit an exact spot on the front steps -- otherwise, the Death Eaters would be able to see the person(s) coming or going.
ETA: The Taboo Curse seems to have done its job at Hogwarts because it would seem that the enchantments protecting Hogwarts were broken -- Professor McGonagall had to refortify the protective enchantments:
‘You’re acting on Dumbledore’s orders?’ [Professor McGonagall] repeated, with a look of dawning wonder. Then she drew herself up to her fullest height.
‘We shall secure the school against He Who Must Not Be Named while you search for this – this object.’
‘Is that possible?’
‘I think so,’ said Professor McGonagall drily, ‘we teachers are rather good at magic, you know. I am sure we will be able to hold him off for a while if we all put our best efforts into it. Of course, something will have to be done about Professor Snape –’
Deathly Hallows - page 479 - Bloomsbury - chapter thirty, The Sacking of Severus Snape
It's interesting that Professor McGonagall continues to call Voldemort "He Who Must Not Be Named" even though the Taboo has already been broken (see the quote in alexwlchan's answer). I wondered for a moment if this means the Taboo was actually not broken, because Hogwarts, I think, would be the one place where it might be possible for protective enchantments to remain intact in the face of the Taboo Curse, but the fact that they have to refortify the castle's enchantments really doesn't support this theory. I think perhaps McGonagall used "He Who Must Not Be Named" out of habit. My first quote does state that Dumbledore really was the only person to openly use Voldemort, until Harry started doing so as well.
ETA: The Goose rightly points out in the comments that No. Twelve Grimmauld Place was under the protection of the Fidelius Charm, as headquarters for the Order of the Phoenix, so while the Taboo Curse did work, and broke the enchantments protecting Harry, Ron, and Hermione's location, the Fidelius Charm prevented the Death Eaters from seeing the trio or others going in and out of Grimmauld Place and from entering the premises.
The Taboo is still in effect in Hogwarts and Hogsmeade.
From Deathly Hallows, chapter 30:
“Yeah, I do,” Harry assured her. Somehow her panic steadied him. “Professor McGonagall, Voldemort’s on the way.”
“Oh, are we allowed to say the name now?” asked Luna with an air of interest, pulling off the Invisibility Cloak. This appearance of a second outlaw seemed to overwhelm Professor McGonagall, who staggered backward and fell into a nearby chair, clutching at the neck of her old tartan dressing gown.
“I don’t think it makes any difference what we call him,” Harry told Luna. “He already knows where I am.”
Harry and Luna both seem to suggest that using his name will alert Voldemort to Harry’s presence in Hogwarts. They don’t name it as such, but this is the definition of the Taboo curse.
Nobody else up to that point, in Hogsmeade or Hogwarts, has used his full name in the text. We see similar charms in Hogsmeade – for example, the Caterwhauling Charm that Harry et al. set off when they apparate into the village – so it seems logical that the Taboo would also be in use.
(At this point, Voldemort doesn’t really need the Taboo to find Harry – one of the Carrows has pressed their Dark Mark – and Harry and Luna could have heard of the Taboo from their time outside Hogwarts, and it not be in effect within the castle – but there’s no compelling reason not to apply it in those two locations. It seems logical that the Taboo would still be in effect.)