Exactly how many title reigns a person has had is a matter of some debate. I prefer to use the Pro Wrestling Illustrated list as they are neutral. They only consider a title to be a World title if it has significant international television exposure at the time. "World" title status can, therefore, be granted and revoked - for instance, the ECW Championship was considered a world title but isn't anymore and the NWA World Heavyweight Championship lost it's world title status, regained it when it started being defended on TNA and then lost it again when TNA severed their ties with the NWA.
WWE and TNA have different ideas, hence Ric Flair being announced as a 16 time champion despite actually having 17 reigns and the utter bullshit that is the "12 time Champion" Kurt Angle. No, Kurt, Olympic gold medals and world titles in amateur wrestling do not count!
The current PWI recognised world titles are the WWE Championship, the World Heavyweight Championship (both WWE) and the TNA World Heavyweight Championship. PWI formerly recognised the AWA, NWA, ECW and WCW World Heavyweight Championships.
Ric Flair is an 8 time NWA, 6 time WCW and 2 time WWE champion.
Hulk Hogan is a 6 time WCW and 6 time WWE Champion. I think they are recognising his WWE Undisputed Championship reign as one WWE Championship reign.
Triple H is a 7 time WWE Champion and a 5 time WWE World Heavyweight Champion. I do not recall Triple H winning either title twice in one night. Randy Orton "won" the WWE title twice at No Mercy 2007 where he was awarded the vacant title, immediately lost it to Triple H and then won it back later that evening.
Behind them are Verne Gagne (10x AWA), Jeff Jarrett (6x NWA, 4x WCW) and Sting (2x NWA, 2x TNA, 6x WCW) on 10 reigns.
For the record, Kurt Angle is, in fact, an 8 time champion - 2x TNA, 1x WCW, 4x WWE, 1x WWE World.