...but Wolverine does have bone claws, that's one of the things they got right!
In X-Men #25 (one of the ones with the hologram on the cover) Magneto starts going crazy with power, Wolverine rips open his chest which rightly pisses Magneto off, Magneto rips the adimantium out of Wolverine. Later in Wolverine #75 in a pretty cool moment Wolverine goes into his I'm still the best at what I do and what I do isn't very nice nice bit as he tries to extend his claws for the first time since and ends up pushing bone through his skin.
Now how he got his metal back, I don't know. I had stopped reading comics by that point.
This is an Answerbag answer to the question:
Yes, actually, Magneto did once remove Wolverine's adamantium.
In response, Xavier lashed out with a powerful psychic assault that wiped Magneto's mind, and left him a drooling vegetable for months.
Wolverine nearly died, but his healing factor saved him. Once the adamantium was out, Wolverine discovered that his healing factor was greatly increased. And soon, in a conflict with Cyber, Wolverine popped bone claws from his hands for the first time, proving that claws were one of his mutant powers all along--they were just covered with adamantium, like the rest of his bones.
Of course, the bone claws were much less durable and would tend to break off in combat, which hurt like nobody's business. But Wolvie's used to pain and would just grow more.
Soon after, Wolverine was captured by a rather obscure character called Genesis. Genesis was really Tyler, Cable's son from the future who had gone insane and evil. Tyler wanted to be the heir to Apocalypse, and so created armor that kind of made him look like Apocalypse. Genesis gained control of the Dark Riders, and then captured Wolvie's old foe Cyber, who had admantium cybernetic arms. Genesis threw Cyber into a pit where these flesh-eating beetles...well, let's just say when it was all over, the cybernetics were picked clean.
Genesis then tried to re-bond the adamantium to Wolverine's bones, but it didn't take--Wolvie's healing factor went into overdrive, which put him into the mother of all berserker rages, during which he killed Genesis and most of the Dark Riders (except for Tusk, of course, the only slightly cool one).
Years later, the real Apocalypse returned and captured Wolverine. He pitted Wolverine against Sabretooth, who at that point had adamantium on his bones (it isn't clear where Sabretooth got this treatment, but it was around the time that he was working with the government-sponsored X-Factor, so Weapon X is the most likely supplier). The winner of the contest would get to be Apocalypse's new horseman, Death. Wolverine didn't want to be death, but reasoned that Sabretooth would be even more murderous and unstoppable as Death, so Wolvie gave it his all and beat Sabretooth. As a reward, Apocalypse removed Sabretooth's adamantium and bonded it to Wolvie's skeleton, and this is the adamantium Wolverine has had ever since.
Later, Sabretooth started dying because his body could not adjust to the absence of the adamantium. Gambit found him and arranged for Sabretooth's old partner, the Constrictor, to part with his adamantium tendrils, which were melted down and bonded to Sabretooth's bones.
So now both Sabretooth and Wolverine have adamantium.