X different Opening Day Starting Third Basemen in X Seasons (since 1914)
Baseball-Reference takes us back until 1914 and while Retrosheet provides starting pitchers in their game logs, it doesn't have that for other positions.
The Dodgers were very successful in their final seasons in Brooklyn and their first few in L.A. despite the turnover at third. The nine-player streak for the Browns/Orioles ended in 1958 when Brooks Robinson made the second of 20 consecutive Opening Day starts. The longest active streak belongs to the Angels, but with David Freese slotted at the hot corner again, it will likely stop at six (after Chone Figgins, Brandon Wood, Maicer Izturis, Mark Trumbo, Alberto Callaspo).
Here's the full list of third basemen from the teams shown above. Some interesting names here include the trio on the Sibby-Nanny-Skippy 1938-47 Braves and two longtime outfielders that turned up on the list, Bobby Murcer and the late Minnie Minoso. There's also Cookie Lavagetto, who broke up Bill Bevens' 1947 World Series no-hitter with a walk-off double; and Bob Dillinger, the last third baseman to lead his league in stolen bases (20, 1949 Browns). The most surprising name I saw was Bucky Walters. He was a standout right-handed pitcher and won the 1939 MVP for the pennant-winning Reds, but I didn't know he came up as a third baseman with the Braves. In the September after his 1934 Opening Day start with the Red Sox, he made his mound debut with the Phillies en route to 198 career wins and the 1939 N.L. MVP Award.