Attack Speed is capped at 2.5 attacks per second, but there are a couple effects in the game that can temporarily remove this cap.
Cooldown Reduction is capped at 40%, with a rune that increases it further by 5% (plus another rune that independently lowers the cooldown of your ultimate ability).
Critical Strike Chance is capped at 100%.
Movement Speed has two soft caps. Every point after 415 but before 490 is reduced by 20%. Every point after 490 is reduced by 50%.
There are no other stat caps I can think of, except possibly Tenacity and Slow Resistance, increases to which will shrink as the total approaches 100%. Possible exceptions are Master Yi’s Highlander and Olaf’s Ragnarok, but I don’t know if they manipulate the stat to get their results.