Gov. Tom Corbett of Pennsylvania said Wednesday that he would not appeal a judge’s ruling striking down Pennsylvania’s ban on same-sex marriage. With the decision, Pennsylvania became the 19th state, along with the District of Columbia, where same-sex couples are able to marry. Judge John E. Jones III of Federal District Court on Tuesday became the latest judge to throw out a series of state bans around the country, writing, “It is time to discard them into the ash heap of history.” Mr. Corbett, a Republican facing a difficult re-election this year, announced his decision the day after Democratic primary...