Can anyone with a camera shoot whatever he wants? Is there any license or permit that is given to a photographer? Or should a photographer take the permission of the subject he shoots (if it is a person)? Let the country be US.
Short answer: no. You can't just take pictures of whatever you want.
As others said, you need to contact the local jurisdiction for where you are going to take photographs. And you need to be specific in any request. For example, it is generally considered acceptable for a person to shoot a casual shot or two in Venice Beach. But if you're doing paid work or setting up a crew, etc. you need a permit. In general, private property always requires the permission of the owner. In general, public property in the US is open access except where the local ordinances require a permit. Military and sensitive locations are generally considered off limits. Additional restrictions may apply in some places (such as power plants, power lines, railroads, etc).
It is the photographer's responsibility to have all the legal issues addressed before starting any commercial work. And whatever is true in one place does not mean it is true anywhere else. Some people operate by the "ask forgiveness rather than permission" principle. And often that works but when it doesn't work the consequences are usually worse than if they went through the process at the beginning.
Also keep in mind, in the US since you mentioned it, that model releases and property releases may be required for any commercial use. That has to be arranged with the people involved. Compensation may be required.
That would depend (even for the US) on who/what you're shooting, as well as the purpose the photos will be used for afterwards.
This question has a lot of nuance to it, and is something I've done quite a bit of research on. I still don't have a complete understanding of the picture (ha ha), but here's what I've been able to gather so far (note that any answers in this question are only applicable in the US). There are basically two things you have to consider -- what can you legally photograph, and what can you do with the photos once you've taken them? I'll talk about both (keep in mind that IANAL, but I'll try to provide references and citations where I've found them).
The first question is, "What can you photograph?" The key standard for what you can take pictures of in the United States falls under the "reasonable expectation of privacy" domain. The basic rule here is that if the "average person" has a "reasonable expectation" that he won't be observed, you cannot photograph them. What this boils down to is the following -- if you are out in public, you can be photographed by anybody at any time, and the photographer does not need to ask permission. Even if you are on private property, but it is generally considered a public place (such as a shopping mall), photography is allowed unless the property owners specifically state otherwise with signs or markings.
This means that, in particular, as long as you are in public, you are permitted to take pictures of whatever you can see, including any people at all. You may even take pictures of people's houses, if you are on the street, and even inside people's houses if they have large windows open that are visible from the street. (Generally speaking, a person's home is where he has the most expectation of privacy, but if the person does not make an attempt to conceal himself in his home, by closing his blinds, then he can be photographed inside his house).
There are some things that can't be photographed (some military installations, inside airports, etc.), but these are few and far between in US law. For more information on this, see this post by someone who claims to be a photo attorney, this Wikipedia article (which has at least some sources cited), this blog post by Bruce Schneier (who generally knows what he's talking about), and The Photographer's Right document, which you can print out and carry around with you, detailing what you are and are not allowed to do with your camera.
Of course, it (hopefully) goes without saying that what you are allowed to photograph legally and what is a good idea to photograph are two entirely different things.
Now I'll talk about the second part of the question, which is what you are allowed to do with your photos once you've taken them. If the photo doesn't have a person in it, you can do whatever you like. Sell it, plaster it over Facebook, etc. If the photo does have a recognizable person in it, things become a little bit murkier. It's a big question of "Do I need a model release form to sell/display/print a photo with someone in it?" Again here, generally speaking the answer is "No!" The only time you need a model release form is when the photo is being used in a commercial application -- i.e., for advertising purposes. If you want to post the photo on your blog, you can do so with no repercussions. Even if you sell the photo as a photograph (not to be used in advertising materials or on websites, etc.), I believe you're generally ok without one.
Furthermore, usually it is up to the publisher of the photograph to determine when a model release form is necessary, not the photographer. If the publisher needs one for a photo that you take, and they don't have one, the publisher will be liable, not you. The only situation in which this is different is if you, the photographer, claimed to have one, or used one that is not applicable. Then it is possible that you will be held liable instead.
You can find out a lot more information about model release stuff at this website, which is horribly-formatted but has a ton of very detailed information.