Aamir Khan has won one National award for acting but not best actor. He won the National award special mention award for QSQT and Raakh. In the beginning of his career he largely did romantic films. The films where he gave commendable dramatic performances include-
Jo Jeeta Wahi Sikandar (1992)- Mithun Chakraborty won the National award for Tahader Katha. Tahader Katha was more socially relevant film based on the disillusionmemt of a freedom fighter after independence.
Rangeela (1995)- Rajit Kapoor won the National award for playing Mahatma Gandhi in the film The Making of Mahatma directed by Shyam Benegal. The film was an important piece historically so prefered for the award.
Sarfarosh and 1947 Earth (1999)- This time Aamir made socially relevant films but Mohanlal gave a masterclass performance in Vanaprastham. One of the greatest performances in Indian cinema truly deserved the National award.
Lagaan and Dil Chahta hai (2001)- Very curuous to see Murali winning the award for Neythukaran, a left oriented politically charged film, that too during NDA rule and that too at a time when the National award jury was blamed to be politically biased in giving awards (the controversy happened in 1999, 2000 as well as 2002, 2004). I havent seen the film so can’t really comment how good or bad the film was.
Rang De Basanti (2006)- Soumitra Chaterjee after being overlooked so many times and after him rejecting the consolatory National award in 2000, he won the National award for Best Actor finally after so many decades of working with greatest filmmakers of Indian cinema. Anyways Rang De Basanti was an ensemble film with no defined lead actor.
3 Idiots (2009)- Amitabh Bachchan won the Best Actor for Paa. Ranbir Kapoor was also in consideration for Wake up Sid and Rocket Singh. But the steongest contender was Mamooty for Kutty Srank but he lost by 1 vote to Amitabh.
Dangal (2016)- One of the worst choices made in a year. We had so many great options. I was rooting for Manoj Bajapyee to win for Aligarh. We had Aamir for Dangal, Srk for Fan, Sushant for Dhoni all Hindi films (not to forget the films of all other languages) that were way better than Akshay Kumar for a cringe film like Rustom. I wont say that Aamir should have won the award. Dangal was a very nice film but purely as performance i would rate Manoj Bajapyee way above and i also as a performance SRK in Fan was really good.