Before I begin - there are some spoilers in here. Since the basic plot of this book has been imitated so often, though, I don't expect it will spoil things for too many people. It's like worrying about ruining the "chicken crossing the road" joke for someone ...
This is a tough one. Fantastic Voyage is a classic, and it is written by Asimov, a giant in his field. And, frankly, I didn't find it all that impressive. Now, this is partly no fault of the author. The fact is, were I reading this when it first came out, the novel concept of shrinking people down and injecting them into a human body might have really floored me. Unfortunately, many years later, I've not only seen the movie adaptation, but also many, many rip-offs of the concept, the latest being in an episode of Phineas and Ferb (which I highly recommend).
So, the first problem is certainly no fault of the author. Unfortunately, the first problem is exacerbated by the second problem, which is only due to Asimov - the characters are so wooden and hollow that plodding through half of the book waiting for them to be shrunk is just mind numbingly boring. The characters aren't just stereotypes, they are stereotypes of stereotypes. And after the stereotypes are finally miniaturized and injected, the book really doesn't get much better. The description of the human anatomy from the point of view of the miniaturized explorers is sometimes interesting, but occasionally difficult enough for me to picture that any wonder was just lost. But then every step of the story involves entering a new part of the anatomy, introducing the "problem" and then solving said problem, often in obvious ways.
In one important way, Fantastic Voyage was way ahead of its time. Just as many (okay, most) modern movies sacrifice story to special effects, Fantastic Voyage ignores compelling (hell, even mildly interesting) characters and conflicts for the supposed wonder of seeing white blood cells up close. For me, the anatomy lesson and the make-believe physics of the miniaturization process just wasn't enough. If you haven't read the book, I recommend sticking with the movie.
And now I need to finish my Beastmen of Nabu article and then get busy with the illusionist, a low-level adventure set in the catacombs of Ophir, and I need to begin plotting out the next chunk of sandbox ...