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?
Based on this source I would say that those are the only ones.
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.
This source explicitly states that 13O and 7P are the only exceptions in Riichi.
A Winning hand is, except for two exceptions, composed of four MELDS (mentsu [面子]) and a PAIR (jantoo, [雀頭]). The two exceptions are the SEVEN PAIRS (chiitoitsu [七対子]) hands (covered in a later section) and the THIRTEEN ENDS (kokushimusoo [国士無双]) hands (covered later in the special hands section)