I think it's going to be the 1x12 (#60479) and 2x16 (#4282) for regular Lego plates. The next longest plain-ish plate is probably the 6x28 (#5301, 5309, 4093), but these are thicker than typical plates.
For regular tiles I think the 1x8 (#4162) and 2x4 (#87079) are the longest. Outside of the 2x? they made some odd-ball Scala tiles at 3x6 (#6934) and 8 x 20 x 2/3 (#6923). Then there's the big 8x16 (#48288, 90498).
Does Modulex count since it's a Lego company product? There were Modulex 1x16 (MX1616M) plates and 2x12 (Mx1012) tiles. They also made a huge 22x60 (Mx2420D) plate according to Bricklink. Of course these pieces are only longer in terms of studs, because of the smaller scale, the Modulex bricks are not longer in millimeters/inches. I'm curious if anyone has one of the 22x60 plates on hand to verify the bottom type? Then of course there are baseplates, I guess I assumed you weren't referring to those.