From the Wikia itself
S-rank - assigned to experienced jōnin and concern state-level confidential matters. Examples are assassinating VIPs, and transporting highly classified documents. The reward for an S-rank mission is more than a million ryō.
"S-rank" is also a designation given to extremely powerful missing-nin, earning them a place in their village of origin's Bingo Book. The organisation Akatsuki was stated to be comprised mostly of S-rank criminals.
Keeping this in mind we can list down plenty of missions undertaken which would've been classed as S-Rank. Thus off the top of my head the following missions should've been S-Rank even if explicitly not told so.
Retrieval of Gaara: Clearly a S-Rank mission with Team Kakashi and
Team Guy taking on Akatsuki members Diedera and Sasori
The hunt for unnamed Akatsuki - Hidan and Kakuzu. Several squads of
capable Jonin and Chunin were chosen for this S-Rank (not mentioned
This mission led to death of a Senior Jonin Asuma.
Hunt of Hidan and Kakuzu: Shikamaru's planned mission to kill Hidan
and Kakuzu. Not official, but Tsunade allowed Kakashi to go along.
The hunt for Sasuke: Nearly all the original 12 Genin, kakashi,
Yamato etc. hunt for Sasuke. Sasuke is a S-Rank missing Nin, even if
Leaf doesn't consider it. Again not explicit.
Edit: - Interception of Akatsuki spy may have been S-Rank, but I feel it would most probably be a A-rank. Even though they fought Orochimaru
- The unofficial S-Rank mission given by Kakashi to Shikamaru, Naruto
and Sakura (With Pakkun): Follow Sasuke and Stop the Sand Genins. Might've been A-Ranked. Pardon my memory. Putting in the Edit box for now.
Wiki also adds,
These missions are exclusively assigned to highly skilled jōnin or large squads of ninja
This is true for almost all these missions.
Source: Narutopedia's link on S-Rank