Talk with the students who are unmotivated and get to the heart of the matter. Your knee-jerk reaction may be to browbeat them in some form or fashion out of anger, but this can sometimes lead to their not caring even more. Each student has his own reason for not caring, and you should talk with him in confidence about the source of his apathy.
Show the real-life applications and benefits to learning. The classic student response to tedious subject matter is often of the "when are we ever going to use this" variety. For example, algebra tends to fall in this category. Even if the students who don't care will never use the math discipline in their future careers, make it known the importance of learning a system and sticking to it will still bode them well, even if it's not math-related.
Reward the students and give them incentive for caring. There are several ways to go about this. You can start by offering them extra credit for fun yet educational activities. For example, attending an IMAX show about space exploration could garner them extra credit if you're teaching about astronomy. Eventually, the non-caring students should learn that education in and of itself is its own reward, but adding a little extra incentive at this point is fine to get the ball rolling.
Involve the students in the lessons by encouraging participation. While it has a place, sometimes the staid lecture format can turn students off, especially those who don't care. Group activities, fun presentations and discussion forums are all examples of things that will freshen up the classroom and encourage the students to care. Even if it's awkward for them at first, perhaps due to shyness, they will eventually get the hang of it and embrace the challenge.