Derek Jeter, NYY AL, has had one of the best streaks of hitting in major league history, despite little fanfare;  he's had:

54 games with a hit out of 56 games total (six overlapping streaks, last one 8/25/2006-5/3/2007(G2)
--MLB record is 56/56 by Joe DiMaggio in 1941 (a 56-game hitting streak); next best is 55/56 (Dahlen, 1894).  Post-1900 record is now Jeter's, next highest since 1900 was 53/56.

92 games with a hit out of 100 (18 overlapping streaks, last one 8/27/2006-6/23/2007)
--MLB record is 93/100 (Keeler, 1898-1899).  Post-1900 record is now Jeter's, next highest since 1900 was 91/100.

135 games with a hit out of 150 (seven overlapping streaks, last one 7/2/2006-6/23/2007)
--AL record is also 135/150, by Ty Cobb 1910-1911.

146 games with a hit out of 162 games (three overlapping streaks, last one 6/16/2006-6/23/2007)
--AL record was 143/162, by Cobb 1910-1912.

175 games with a hit out of 200 games (9/30/2005-5/25/2007)
--AL record is 176/200 by Cobb, 1911-1912.