Before addressing the main question, let us understand that awards or conferment of titles are not always strictly and directly linked to performances. Even the redoubtable Leonardo DiCaprio who won his first Oscar this year did so for an above average performance and not for one of his highly acclaimed performances which failed to win any award despite regular nominations. In the Indian context, this hit the ridiculous nadir in the year 1971 when the South Indian matinee idol M.G.Ramachandran won the National Award for Best Actor for his nondescript role in a mediocre film Rickshawkaran leap frogging the outstanding performance of Rajesh Khanna in his role of a life time in Anand.
Many a time the awards are results of extraneous considerations or intense lobbying. Even in respect of Kamal Haasan, who won Three National Awards for Best Actor for Moondram Pirai (1982) Nayagan (1987) and Indian(1996) I consider only his performance in Nayagan as award worthy. Moondram Pirai was a syrupy sentimental melodrama, which anyway belonged to Sridevi and Balu Mahendra than to Kamal and in Indian the role of the older Kamal was prosthetically and cosmetically aided stylized hamming.
In my opinion Kamal showed a lot of spontaneity and sensitivity in some of his earlier day films, and brought into play his maturity and intensity in some of his middle years movies. So, in my opinion, the following performances of Kamal Haasan were certainly award worthy, but which did not fetch him any awards :
16 Vayathinile (1977)

Aval Appadithan (1978)

Varumayin Niram Sivappu (1980)

Gunaa (1991)
Thevar Magan (1992)
Mahanadi (1994)

Some other honorable mentions of Kamal Haasan's roles are Sagara Sangamam (1983), Saagar (1985), Swati Mutyam (1986) and Anbe Sivam (2003) which were all excellent, but not exceptional performances. But in my opinion Kamal Haasan also richly deserved a National Award for Best Direction for his following Magnum Opus.
Hey Ram (2000)
