Electricity and cable are not illegal monopolies because they are heavily regulated by the government. While you do not get to personally choose your electric or cable company, your elected officials do. The main reason for lack of choice is that so much infrastructure is required that it doesn't make much sense for multiple companies setting up multiple infrastructures (imagine 13 different sets of power lines running through your neighborhood).
Some states have deregulated utilities, with mixed results. You may have heard of rolling blackouts here in California. The reason for that was deregulation of the state's electricity. Any company could own and sell power and power plants. A lot of out of state power companies bought our power plants, shut them down, and sold what little electricity was left to us at a high premium. Electricity was so scarce that we were faced with rolling blackouts, which fortunately didn't last long because people started conserving energy hardcore. Things have gotten more stable here, but we still get rolling blackout warnings during heat waves. So, in the case of electricity at least, a regulated monopoly is a much better option than a deregulated competition.