Sólyom László (2005-2010)
Again a jurist, professor, member of the Hungarian Academy of Sciences, and as I already wrote member of the Constitutional Court. Sounds serious. I remember the media depicted him an a good light and generally everyone was ok with him. Originally a founding member of the MDF, but when he was appointed into the Constitutional Court he gave up all of his offices and quit the party as well. He was elected to president of the CC.
When he got his position as a Head of State he was unofficially nominated by an NGO, which, I dunno, does stuff, they do some environmental, green activism. His official candidacy was backed by Fidesz and MDF. His election was exciting, as exciting as such can be. The election of the President is a three round process, in the first two, it needs a 2/3 to elect a new Prez, in the third a simple majority is enough. He was elected in the third, the governing parties were divided, the minor coalition partner (the SZDSZ at that time, which managed to slide down from the respectable second biggest party to a mere 5 percenter, barely in the Assembly party) didn't support anyone.
He referred to himself as an independent candidate all along.
He did some controversial stuff. He was very active sending laws to the Constitutional Court, or back to the Parliament for further discussion. Criticized the political leadership after the 2006 protests, refused to give a merit (a high one) to the socialist PM of 1994-1998, Horn Gyula, because that dude was a petty communist thug back in the Rákosi-era, who shot at the revolutionaries in 1956... He also suggested holding a new election during the 2009 governmental crisis. He was in the center of some issues in foreign relations as well. He stated he won't visit the United States as long as they fingerprint Hungarian citizens. Northern Hungary declared him a "security risk" and refused his entry to their country when he was invited to an inauguration of a statue (of king Saint Stephen).
In 2010 his mandate ended, and legislative elections came as well. Fidesz won. Civilians lobbied for his re-election. I don't know if his controversial actions meant a risk, but Orbán wanted someone more placid instead. So we arrive to...


Schmitt Pál (2010-2012)
Sportsman, won two Olympic gold medals in fencing (and some World Championships). He remained at sports for a long time was the vice-president of the International Olympic Committee, but was diplomat, ambassador in various countries.
In Hungary's politics, he started out as quasi-independent, Fidesz backed, candidate for the office of Budapest's Lord Mayor. Previously he tried to get this position, that time he sought help from the Socialist Party (MSZP), but was sent to Bern as ambassador. Then before he was elected as President, he was a member of the Europen Parliament, in the colors of Fidesz, in fact he was a vice-president in the Fidesz during those times.
In 2010 the legislative election, and the election of a new President coincided, so the freshly elected Fidesz-KDNP - backed by over the two-thirds of the seats they won - put its own man into the seat of the head of state.
However it turned out he copypasted much of his doctoral dissertation back in 1992, and after the scandal he resigned.
Absolute puppet of the Fidesz.