Good points by everyone, and I won't repeat my views on some of the specifics such as whether or not Michael blamed Tom for Sonny and the attempt on Vito, as well as the perury trap.

The essence of the relationship aside from Michael's desire to control and manipulate everyone was there was a latent sibling rivalry between the two. As the youngest son, and the most rebellious, Michael grew up seeing Tom being close to Vito, probably closer than nimself, Fredo and possibly Sonny, and this was something Michael resented. He understood Tom was bright and a talented lawyer, but this probably made him resent him all the more.

One of the telling lines of all this is when he tells Kay that Tom is going to be named consigliere...when he does so he makes it a point to say that Tom is not a Sicilian, and he says it in a disparaging way. He even looks away from Kay when he says it. Implicitly he is saying he doesn't think Tom is the right choice, but instead is getting the job because of Tom's closeness to Vito.