I live in US and I am applying to graduate school.I wonder if it is a good idea to send an email to graduate school professors and mention that you like their research and would like to join their research labs?
While you live in the US, you didn't specify whether you are applying to schools only in the US. And the answer depends.
Outside the US, especially Europe, quite frequently PhD positions are funded by individual professors. In these cases the hiring/admission decisions are made almost entirely by the professor in charge of the "group", and so the answer to your question is an "Of course!" There simply is no way to get your foot in the door otherwise.
In the US, or in countries where a US-style system is the norm, the admission of graduate students are made in committee, and it is not necessary to contact specific professors in the application process. This, however, is not to say that establishing a faculty contact won't help: sometimes it will at least earn your application a more detailed look, and sometimes you will find a person willing to advocate on your behalf during the committee meeting.
In either case, be thoughtful when you craft your e-mail. In the US and elsewhere alike, professors often get e-mails exploring the possibility of doing a PhD. So make sure to do your homework! If you write a letter to Professor X asking about studying Subject A with him, and he has in fact left Subject A and had been working on Project B for the past 5 years, at best he would politely decline and at worst you may have created a bad first impression. Same thing goes for a bland letter stating "I like your research". By default academics are suspicious of empty platitudes: make sure to discuss your background (to show that you are making a somewhat informed judgment) and state what it is particularly that you like about her research.
Furthermore, note that in some/many US schools, incoming graduate students for PhD programs do not formally choose an advisor until one or two years into the program. This has to do in part with the belief that the students should be allowed to see all the opportunities available to them, and the professors have some time to assess the students, to mutually make educated decisions about their partnerships. So you should also weigh your own feelings: are they strong enough that you absolutely must work with this one professor? Or do you have broad enough interests that you may want to hold off deciding until you learn more about the subjects?
Lastly, if geography is not a barrier, instead of just an e-mail expressing interest, you can also consider writing and asking to schedule a face-to-face appointment. Even if you end up not working with the professors, more often than not you will learn something and get some very good advice from the discussion.
Its a very good idea to write to the professor you are interested in working with. However, its very important to do your research and find out everything about them. Do use formal language. And show some insight into their work... "I read your research paper on..., I think it has many applications, and we can expand the research to include.... and my background in... will be helpful". But don't be critical of the work.