Well, I usually give everyone a couple days off during the season, so it's not exactly a streak, but my current 1B/occasional DH has never played less than 157 games in his 8-year career, barring his rookie season. I'm sure there was a DtD injury or two in there, but he's never landed on the DL.
Of course, now that I've pointed that out, he's sure to go down for the year soon.
