It was a rule of evidence that I fully understood in law school: a witness's credibility can be impeached with intrinsic evidence of prior bad acts bearing on truthfulness, even if the act did not lead to conviction. (Evidence that is "intrinsic" comes from the witness's own mouth, rather than from documents or the testimony of another witness.)
Here is an example of the rule: A witness appearing for the plaintiff is asked on cross-examination by the defendant's lawyer whether he was thrown out of medical school for cheating on his exams. To ask such a question, the defendant's lawyer must have a good faith basis for believing this actually happened. If the witness says yes, the jury can use this fact in assessing the witness's credibility. If the witness says no, the lawyer must move on, since extrinsic evidence of a collateral matter (the witness's cheating on exams in medical school) would not be allowed.
That's the majority rule, which is codified in federal courts by FRE 608(b). (The notes to FRE 608 contain a useful summary of the rule.)
Illinois, however, follows the minority rule, as explained by cases such as Podolsky and Associates, L.P., v. Discipio, 297 Ill. App. 3d 1014, 697 N.E.2d 840 (1st Dist. 1998). In Podolsky, the court states the general rule that "the credibility of any witness, including a reputation witness, may not be attacked upon cross-examination by questioning the witness concerning specific instances of her misconduct not leading to a conviction."
The Podolsky court also notes some exceptions, so any lawyer seeking admission of evidence of this kind might want to read the case. The most recent pronouncement of the Illinois Supreme Court on this issue came this month in People v. Santos, Docket No. 94620, June 24, 2004, in which the Court stated that "specific-act impeachment is prohibited in Illinois" and gave a long string citation listing prior Illinois cases to that effect.