I know of only two hands that do not consist of 4 sets and a pair in riichi mahjong: Seven Pairs, and Thirteen Orphans. Are there more?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
This source explicitly states that 13O and 7P are the only exceptions in Riichi.
In some variants you have hands like Knitting (seven cross-suit pairs), Thirteen Grades of Imperial Treasure, and the Wriggling Snake.
This page matches the rulebook I learned from. It describes several others such as Windy Chows, Dragonfly, Heavenly Twins (a special case of All Pairs), Run Pung & Pair, and Red Lantern.
I believe most of these should apply to riichi mahjong as well.