About Germany in particular: there used to be semesterly tuition fees of 500 Euros in most places. I believe that most German states have retracted that law though. There are still administrative fees, but they are usually less than 200 Euros/semester.
Undergraduate degrees are all taught at least partially in German, so you'd absolutely need to be able to speak German. In fact, documented proficiency in German (at the B-2 or C-1 level in the European reference frame for languages) is a requirement for admission.
Most German universities have open admission policies for most of their majors for applicants with a German high school credential. If you have a foreign high school credential, it needs to be deemed equivalent to a German one.
Most Western European credentials (e.g. British A-levels or the French Baccalaureate) are accepted, but not many credentials from other parts of the world. An American high school diploma, for example, would not be sufficient to attend a German university. You'd need at least 4 AP scores in addition to a high school diploma, or alternatively, an American high school diploma plus 2 years' worth of college credits. (To enroll as a first-year student at a German university!)
Some of those requirements trace back to German snobbishness, but some are necessary to protect incoming students. For example, no German university teaches calculus because it's a high school graduation requirement in Germany. Applicants with a high school credential that does not require calculus (e.g. the American high school diploma) need to submit additional documentation (e.g. AP Calculus scores) to document their understanding of the subject.
However, some majors have restricted access: medicine, law and international business degrees in particular are difficult to get into. Since preference is given to German and then to European student, non-European students basically cannot study those subjects in Germany.
In case you are not familiar with the German education system, Germany teaches a smaller range of majors at universities than most other countries. Doctors, lawyers, engineers, teachers, and other such professionals study at universities. However, nurses, accountants and kindergarten teachers are trained through an apprenticeship system. Less than 10% of the adult population in Germany has a university degree. The standard terminal university degree is the Master's degree. (Unlike in the US, where the standard terminal degree is a Bachelor's.)
Germany from what I know requires german except if you are in Jacobs or probably ECLA if you are going for its american degree.
To add to radner's post: Jacobs and ECLA are private American-style universities and charge the tuition rates of a private university.