Can i get in trouble for things i research on the internet?

i dont want retarded uneducated answers and please dont be a smart @ss about it.. i just wanted to know if people can see what ur doing on the internet and if its possible to get pursued in anyway for what you do on the computer. (im not talking about being a pedophile) and im aware they can come in ur house and check it out but can they as ur looking at it? i was looking at stuff kindof like the anarchist cookbook if you know what that is.