I believe that Catholic Hierarchy is currently the best tool for showing apostolic succession.
Keep in mind that written records only exist going back to the Renaissance, and they get spottier as we go back in history.
However, looking at (for example) the page for Cardinal Timothy Dolan of New York, scrolling down past the “events” table and “micro-data summary,” we see that Cardinal Dolan was ordained a bishop by then-Archbishop Justin Rigali. Clicking on (now) Cardinal Rigali’s link, we see that he was ordained a bishop by Pope St. John Paul II, and so forth.
There is another complication to keep in mind with regard to apostolic succession: most episcopal ordinations are acually concelebrations. That is, a minimum of three bishops lay their hands on the ordinand, and all three pronounce the essential words of consecration. The apostolic succession, therefore, could just as legitimately be traced through the so-called co-consecrators (visible just under the “principal consecrator” field). Moreover, there are often more than three concelebrants, and these do not make it into the records.
(The custom of having multiple consecrators—however it arose—has the advantage of removing, for all intents and purposes, all possible doubt as to the validity of the episcopal ordination.)
If you keep clicking, you will note that the vast majority of Western bishops can trace their lineage to a certain Cardinal Scipione Rebiba. (This happened because Pope Benedict XIII, who traced his line to Cardinal Rebiba, consecrated no less than 139 bishops, for dioceses across Europe.) Unfortunately, we do not know who ordained Cardinal Rebiba a bishop (though there is no doubt that he was an auxiliary bishop in Chieti, Italy, and later archbishop of Pisa), so the written records largely stop there.