Willie Taveras's current hitting + getting hit streak is 4 games longer than Craig Biggio's longest such streak, which was 27 games stretching from May 23, 2001 to June 23, 2001. Biggio's streak included an 18 game hitting streak and 2 games in which he was plunked but did not have a base hit.
Of the 42 hitting streaks of 30 games or longer, only 2 are known to be extendable by including HBPs. Taveras's ongoing streak, and Albert Pujols's 30 game streak of 2003 - which was actually a 31 game hitting + get hitting streak. (However, there are 22 streaks on the list for which retrosheet.org doesn't have game by game data, so their could be more.)