My high score is 508. The top scorer on the leaderboard is ikkejessica with 1988. Very impressive.
Theoretically, one game, played perfectly, could go on forever, I think. Similar to Stickets. Although I think Stickets is more elegant and sophisticated.
I should mention that Four Straight Lines is FREE.
Update 3/1/15: There are only 469 players on the Leaderboard. The high scorer has 4860 while the second scorer has 2832. Very impressive. ikkejessica has fallen to #25.