Anyway, if we're considering "parties which have a chance of forming government" as major and limiting it to only democratic systems:
Fidesz (Hungary)
Republican Party (United States)
BJP (India)
ANC (extremely sad to put them on this list, but in their modern form they count)
LDP (Japan)
PRI (Mexico)
Likud (Israel)
The above are in no particular order. There are probably more that I'm not thinking of right now.
Some other pretenders:
Party of Regions (Ukraine)
FJP (Egypt)
PdL (Italy)
Law and Justice (Poland)
Justice and Development Party (Turkey)
If we include countries that can hardly be called democracies but nevertheless aren't one-party dominant states then 1st place goes to Hezbollah or one of the Iranian conservative parties.