Character matters.
It does. But it's tricky. Because a person is of bad character, doesn't mean they committed any particular act they're charged with. If you were charged with a crime, can you think of enough things from your past, that if offered against you, might make you look less than savory, if presented as snapshots in time?
While it's not a perfect system, I'd rather err on the side of just trying the evidence at hand, than trying to convict people because I can convince 12 people they're of bad character, or simply unlikeable, and therefor must have done what they're charged with.
Not all evidence of bad character or bad acts is excluded.
Here's the rule:
RULES OF EVIDENCE
Article IV. RELEVANCY AND ITS LIMITS
As amended through January 1, 2012
Rule 404. Character evidence not admissible to prove conduct; exceptions; other crimes, wrongs, or acts
(a) Character evidence generally. Evidence of a person's character or a trait of character is not admissible for the purpose of proving action in conformity therewith on a particular occasion, except:
(1) CHARACTER OF ACCUSED. Evidence of character offered by an accused, or by the prosecution to rebut the same;
(2) CHARACTER OF VICTIM.
(A) In criminal cases. (i) Evidence of a pertinent trait of character of the victim of the crime offered by an accused, or by the prosecution to rebut the same, or (ii) evidence of a character trait of peacefulness of the victim offered by the prosecution in a homicide case to rebut evidence that the victim was the first aggressor;
(B) In civil cases. Evidence of character for violence of the victim of assaultive conduct offered on the issue of self-defense by a party accused of assaultive conduct, or evidence of character for peacefulness to rebut the same;
(3) CHARACTER OF WITNESS. Evidence of the character of a witness, as provided in Rules 607, 608, 609, and 616.
(b) Other crimes, wrongs, or acts. Evidence of other crimes, wrongs, or acts is not admissible to prove the character of a person in order to show action in conformity therewith. It may, however, be admissible for other purposes, such as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident, provided that upon request by the accused, the prosecution in a criminal case shall provide reasonable notice in advance of trial, or during trial if the court excuses pretrial notice on good cause shown, of the general nature of any such evidence it intends to introduce at trial.