The act for which Odysseus is most famous occurs in the Iliad, when he designs the Trojan horse to sack Troy.
In the Odyssey, this character is again renowned for his ingenuity. He manages to connive a way to get around the Sirens and Circe with his wits.
The most outstanding achievement featured in the Odysseyis probably his homecoming in which he both outwits and out-battles the suitors who have attempted to claim ownership of his kingdom.
I would say that Odysseus is also known for his strong desire to achieve his goals. He could easily have stayed in a number of different places rather than trying to return to Ithaca. His drive and determination is also one of his major characteristics.
To ask what Odysseus of Homer's "Odyssey" is most known for is to ask a question about what is known to literary critics as "reception" studies. This is essentially an historical question that can be answered best by fully tabulating all later mentions of Odysseus in literary works and analysing the frequency of occurrence of different characteristics, episodes, etc. That work has not been done in depth.
The characteristic for which Odysseus is most known is cleverness. his most common epithet is the wily or many-devising Odysseus. The best know plot element is his determination to return to Ithaca and Penelope.