The traditional answer is obviously a half (or halfback more specifically). Though I think it's a difficult one to answer, and as facey has stated, the changing game means it's probably a question that has a different multi-faceted answer every year. It also probably prompts a look at teams individually. Without a doubt the fullback role has evolved in recent times, with fullbacks often being central to attacking plays. Storm and Dogs being the obvious examples of teams that have FB's that are of equal importance to any other position in the side. It's difficult to separate who is the 'most' important of Smith, Slater, Cronk - and the overall answer is they're probably just as important as eachother to their setup. Certainly that setup is geared towards utilising all 3 together rather than any 1 of them as the be all end all. Barba and the Dogs is a little more clear cut, though their style is quite different. I think the Dogs are probably more the exception rather than the rule however.
Dummy half is another position that has become just as important as the halves in some teams. Deviating from the Storm example, I'd argue that Robbie Farah is on Marshall's level in terms of importance to the Tigpies structure. He and Smith are probably out on their own in terms of out and out influence, but there's no doubt that an influential dummy half will go a long way to success - especially if they're able to develop a combination with the halves/fullback.
I've had a couple discussions with people re this topic, and I think overall, the answer is probably still that at least 1 'dominant' half is paramount for NRL success. Below is a list of NRL winners since the year 2000, tagged with who I consider their dominant half for that particular season. There would be an argument for a couple of those teams, certainly Lockyer (as a fullback) in the Broncos side of 2000, and then Cameron Smith in those Storm teams. However I think as a snapshot of the past 10 or so years - a dominant half seems to be the most consistent factor behind success.
2000 - Brisbane - Kevin Walters
2001 - Knights - Andrew Johns
2002 - Roosters - Brad Fittler
2003 - Panthers - Craig Gower
2004 - Bulldogs - Brent Sherwin (Could make an argument for Braith Anasta)
2005 - Tigers - Benji Marshall
2006 - Brisbane - Darren Lockyer
2007 - Storm - Cooper Cronk
2008 - Manly - Matt Orford
2009 - Storm - Cooper Cronk
2010 - Dragons - Jamie Soward
2011 - Manly - Cherry
Evans 2012 - Storm - Cooper Cronk