In the United States, different jurisdictions have different rules about what topics may be addressed in cross examination.
In the federal courts, Fed. R. Evid. 611 generally discourages cross examination on matters not addressed in the direct examination, although it also permits questions on "matters affecting the witness’s credibility."
So if a witness is asked on direct examination only about whether A stopped at the intersection before B crashed into him, the cross examination probably shouldn't go into questions about how severe the injuries were, what the weather conditions were, etc. But the court should allow cross-examination on whether the witness is the plaintiff's sister, or whether the witness was previously convicted of perjury. (Despite the rule, the court has a great deal of latitude as to how to handle these questions, practically speaking.)
In the state courts, the rules may be different. In Ohio, for instance, Rule 611 is roughly identical, except that it generally allows questions on "all relevant matters." So now the questions about the weather and injuries are fair game, along with the questions about the witness's credibility.
In any event, the questions will remain subject to the other rules of evidence, so questions about sexual history might be excluded by the rape shield, and questions about irrelevant matters should be prohibited, as well.