Wolverine has stabbed a number of opponents using his adamantium blades in the movies but every time he does so and takes out the blade from someones' body it's nice and shiny. There's not even a single drop of blood on his blades. Why does that happen?
Specific to the movies, in short, because the film makers don't want to depict too much blood and violence in the film. It probably has a lot to do with the US motion picture rating system.
A film rated PG-13 for "intense violence" is given this rating if blood is present in a violent way
An R-rated movie may have more blood, gore, drug use, nudity, or graphic sexuality than a PG-13 movie would permit.
I'd have to say that the rating system itself is still somewhat subjective-- it depends on how much leeway is given for what is considered violence. Keep in mind that the story around Wolverine is that he's a hero, an X-Man-- not some guy that is slashing everyone with blood on his 'knives' to show for it. It's already plenty violent when he stabs someone, which is how they keep earning a PG-13 rating I'm sure.
History also tells us that PG-13 movies make more money than R movies because it reaches a larger audience. So unless it's really necessary, the director isn't going to depict violence that begins to reach R rating levels.
Also see: MPAA - What each rating means
As a possible answer as to why there is no blood (and this is purely theoretical for the movies) is the fact that his claws are quite keen and never lose their edge, Wolverine doesn't not experience any resistance when 'clawing' an enemy. This it is quite fast. As I am sure we have all experienced, a wound may not immediately bleed, depending on severity, depth, width, tearing, and location. So there is a factor of speed. Also, since his claws are neither serated nor jagged, the cuts are very fine... surgecal, in fact. A fine cut would not bleed profusly at first, as the blood vessels may not have had time to split (read your biology, tendons and blood vessels will pull apart when cut). Flesh wounds with capillary blood is slow and oozing, and may not get blood. Now I agree that an artery would squirt blood all over the place. Yet, it is known that a knife would can sometimes be self-sealing, for a brief moment. Yes, the wound and the body will attempt to seal itself before the blood fills up the space created and come poring out like a dam with a hole. It could very well be possible that the skin squeeges the blood off his claws.
In the comic books, his claws come quite bloody. Then again, Wolverine usually isn't drenched in blood, whic would happen if he, say, started chopping up swat team members in the X-mansion. Because let's be honest. My explaination, while plausible, might work once or twice in a fight. Not every dang time.
Of course, we're talking about the guy who survived being nuked, but can't regrow a hand after Cyclops blasts it off in the Age of Apocalypse.