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The Play Index is the most thorough and powerful publicly available baseball research tool. Subscriptions are normally $36/year. Below is a sampling of some of the search tools:
The Batting or Pitching Season Finder. This tool allows you to search full-season or multi-year totals to find your own custom leaderboards. You can look at the entire history of baseball from 1871-2014 with every year, team, and position available, or you can filter the results in a vast number of ways: by specific years, by age, by first six seasons or last ten seasons, by American League only, by Cubs only, by switch-hitters, by catchers, by outfielder or infielder, by year of debut, but active or retired, by Hall of Famer, by height and weight, by living or deceased, or by a range of common statistical categories. Then you can sort the results by any common statistic, by the teams with the most players matching that category, by players with the most seasons matching that category, or by most recent, youngest, oldest, final year, or year of debut, and others.
The Batting or Pitching Game Finder. This tool allows you to search player game totals (think 4 for 5 with 3 RBI, or 10-SO shutouts) filtering on any of a dozen or more choices. This can be done either on a single player level or on any batter from nearly one hundred years or on any pitcher. The same can be done for Team Batting or Team Pitching Totals.
The Batting or Pitching Split Finder. This tool allows you to search player splits (think most road home runs, biggest lefty/righty splits or most hits in Yankee Stadium) filtering on any of a dozen or more choices. This can be done either on a single player level or on any batter from nearly 100 years or on any pitcher. The same can be done for Team Batting or Team Pitching Splits.
The Batting or Pitching Streak Finder. This tool allows you to search player games looking for the most consecutive games matching a particular set of criteria. This can be done either on a single player level or on any batter from nearly sixty years or on any pitcher. The same can be done for Team Batting or Team Pitching Streaks. Note that when searching for batters, you should limit your searches to 20-25 years when searching through all games.
The Batting or Pitching Event Finder. This tool is player specific and will out put a detailed summary and play-by-play list of all events of a specific type from a single year or an entire career. For example, you can see all of Harmon Killebrew's triples or even his outs to the second baseman.
The Batter vs. Pitcher Tool. This tool presents a complete sortable list of batter or pitcher with totals for every opponent they faced by career or by year. Clicking on the player's name will lead you to a detailed output of their head-to-head plate appearances.