I thought about calling these guys the Anti-Griffey/Mattingly/Longs, after the players holding the record for consecutive games with a home run, but that doesn't quite fit (and it's pretty cumbersome). "Anti-Joneses" is an option, but how many people can identify Chipper Jones as the guy who holds the record for consecutive games with an extra base hit (more on that later)? Maybe "Swatless Swingers" would work, but it sounds pretty corny. Whatever you call them, you can't deny their lack of power.
The longest "active" streak belongs to Orlando Palmeiro (44 games), but he's retired. The next longest current streak is 33 games belonging to Jason Wood, but he's now playing for the Marlins' AAA affiliate in Albuquerque. That means the longest active streak for a player currently on a major league roster is 31 games (through 4/21/08), belonging to Willie Bloomquist of the Mariners. Mark Sweeney of the Dodgers is right behind him at 30 games.