Do you take a polygraph test when you join the police/FBI/CIA/etc?

Before you're hired to work for the government as a cop/FBI/CIA/NSA agent, or even the secret service, do they perform a lie detector test on you?

Also, what do they look for in these tests? Do they want to see if you are honest in your answers, if you're hiding a dark (criminal) secret, or if you have an inappropriate agenda by wanting to join the agency?

Yes, for at least the federal agencies that you mentioned in most circumstances you will be required to undergo polygraph testing. FBI, NSA, CIA, DOE, etc. require Top Secret clearance for most positions.
The first part of the clearance process is filling out the EPSQ (sf86) a very detailed form that goes over approximately the last 10 years of your life. (A Secret clearance requires only 7 years of information to be checked but you will likely fill out 10 years anyway.)
The key elements that the clearance process, and therefore the polygraph test, looks for are security risks. These are risks related to your exposure regarding finances, sexual promiscuity, drugs and alcohol, mental health and foreign nationals. In certain DOJ (FBI) positions you cannot have EVER used drugs, so you will be questioned about that. A TS clearance involves personal interviews with your EPSQ references, so you may be questioned about those. You will be questioned about the things in your EPSQ and any other information they dig up.
The polygraph is one of the final stages in the process. At the end, there is a final adjudication interview where you are interviewed and your clearance is granted. Intense process, rewarding career. Good luck.

In most cases yes but I'm not sure why. All the poly does is give you incentive to tell the truth if you believe that they can actually detect a lie. If you don't believe that, they are useless. I even have some personal experience on it when as a college student, I applied for a couple of security guard positions. First one, told the truth and failed. Second one, had a job lined up so tested the concept: told mostly the truth but told three whoppers and past the test. There is a very good reason why they cannot be used as court evidence :)

They look at squiggly lines to see if some squiggled a lot (I believe there are seven lines per question; one for heart beat, etc) which supposedly indicates discomfort and thus a lie. Some basic questions (with obvious answers) will be asked to determine your baseline.

It depends on what position you are applying for, but generally, they require a polygraph