I am a geek. I've read a large percentage of Wolverine comics, but by no means all. I state this only to demonstrate that I am not merely pulling this out of my *.
There is no point within any of the many titles wherein Wolverine gets something stuck between his claws, that I am aware of. However, there are a few factors that would go into this that might explain why this hasn't happened, beyond the simple matter that showing something like that would be too comedic for the general style of the character.
1) The blades are not fixed. While this is obvious in that they slide in and out, but they are often shown flexing to a greater or lesser extent to the sides. Adamantium is described as being indestructible, but that does not seem to equate to being completely stiff. Even if the blades were stiff, the base of each blade is anchored by tendons and muscles. As such, something would only get stuck if you first spread the blades as far apart as they can go, and only then cutting through something.
2) The blades are shown as being extremely smooth. This means that they would produce very little drag, so again reducing the chances of the blades getting stuck or of something getting stuck in between them.
3) Wolverine is well over 100 years old. He has lost his memory many times* in that period, but never had to relearn how to move or fight. As such, he has a tremendous amount of practice using his bone claws, which, as another user commented, would be far more likely to snag. This means that he would know how to use his claws to minimize anything getting caught in them, most likely by pulling back while cutting. There is, after all, far more space between his claws at the tips than at the base, so anything that might have gotten stuck close to this hands slides right through further away.
*The official(currently) explanation for why he has such memory problems is that occasionally he suffers trauma severe enough to send his body into a form of "healing shock." In this state, his healing factor becomes hyperactive, repairing anything that might count as damage--unfortunately including brain tissue, thus destroying many of his higher level memories while retaining his reflexes and motor control. The Weapon X project is just one example of many situations where this happened, but it does not happen every time he experiences heavy damage.