Q:

Why only Lord Vishnu incarnates on earth?

It is said that there are 3 supreme lords i.e. Brahma, Vishnu and Shiva. But from all 3 why only 10 incarnations of Lord Vishnu and not others?

A:

No. Shiva and Brahma also incarnated on earth. It is indeed Shiva who takes Yogavatar at end of every Dwapara Yuga and beginning of Kali Yuga. 
Most famous Avatar of Brahma is Chandra or Moon God which is explained in this answer. As explained in same answer, Sri Vaishnavas believe Vikhanasa as avatar of Brahma as described in Pancharatra Agamas.
Shiva's incarnations are described in detail in 42 chapters of Satarudra Samhita of Shiva Mahapurana. Some of His famous incarnations are Kala Bhairava, Veerabhadra, Rshba, Nandi (partial Avatar), Hanuman, Sage Pippalada, Drona's son Aswatthama. You can read their legends in detail from Satarudra Samhita which is available here (Chapter1, Chapter2 and Chapter3) and here (Chapter 80- Chapter 121).
Apart from Trimurties, Devas do take Avatars. As mentioned in this answer, many characters in Mahabharata and Ramayana are avatars of Devas like Arjuna being Nara and Indra, Krishna being sage Narayana (who is inturn Lord Vishnu), Karna being Surya, Bhisma being Vasu, Yudistara being Yama, Bheema being Vayudeva and so on.  Number of Avatars of Devas with Avatars of Trimurties are infinite.
So, not only Lord Vishnu, other Devas too incarnated on earth.

