I decided to figure out the longest scoreless inning streak and longest hitless streak. I didn't do it originally because it would have been too much work to find the top 5 for each, having to look through endless play-by-plays of 2010 games. I decided, however, just to find the longest of each such streak, since that was more doable.
Longest Hitless Streak
Most AB without a hit
1. Denard Span: 0-22, 6/1-6/6
Longest Scoreless Innings Streak
1. Francisco Liriano: 23.1 IP, 4/9-4/27