In the United States, the census is officially a big deal (see How the Census Works to learn exactly how big a deal it is). Originally, the census was meant to be a way to count everyone so that the members of the House of Representatives could be allocated properly to the states. Every 10 years there would be a count, and states with more people got more members in the House. Over time, the government has gotten significantly more complicated, and today, the federal government allocates money to states for all sorts of programs. Something like $100 billion gets distributed every year, and quite a bit of it is distributed based on population. The census provides the only official head count.
Someone is very likely to notice if you do not fill out and return your form. After April 1 in a census year, all of the responses received by the U.S. Census Bureau will be compared to major lists of U.S. residences. If your response has not been received -- or if you didn't complete all the questions on your form -- someone from the census will contact you for that information. The census is a $6.5 billion dollar project. They can afford to be thorough!
If you refuse to give out the information or you deliberately give inaccurate information, you can be in legal trouble. According to United States Code, Title 13 (Census), Chapter 7 (Offenses and Penalties), SubChapter II, if you're over 18 and refuse to answer all or part of the Census, you can be fined up to $100. If you give false answers, you're subject to a fine of up to $500. If you offer suggestions or information with the "intent to cause inaccurate enumeration of population," you are subject to a fine of up to $1,000, up to a year in prison, or both. Here's the official verbiage:
Sec. 222. Giving suggestions or information with intent to cause inaccurate enumeration of population
Whoever, either directly or indirectly, offers or renders to any officer or employee of the Department of Commerce or bureau or agency thereof engaged in making an enumeration of population under subchapter II, IV, or V of chapter 5 of this title, any suggestion, advice, information or assistance of any kind, with the intent or purpose of causing an inaccurate enumeration of population to be made, shall be fined not more than $1,000 or imprisoned not more than one year, or both.
221. Refusal or neglect to answer questions; false answers
These links will help you learn more:

