Triple H, like many has said already, is a good worker, performer, and all-round talent (including promos), but he hasn't done anything to really say he is great. Yes, he is "that damn good!" but isn't "that damn great!"
Before Triple H's injury in 2001, as part of the Two Man Power Trip, I was fan of his work as a great heel, and pretty much everything before that. He started having real haters the night he came back from the injury. Triple H will tell you himself that, that night was one of the best of his career - due to the ovation he recieved. That night is when Triple H said to himself "you know what? I'm great!", and then his ego inflated - pushing for himself to dethrone a much more deserving Champion in then mega-heel Chris Jericho at Wrestlemania AFTER he won the Royal Rumble.
After that came his eventual Heel turn and being "awarded" the World Heavyweight Championship by Eric Bischoff on Raw in 2002/3. And from then on, with Austin and Rock gone and Undertaker on the "B-Show" SmackDown, Triple H gained more power backstage and protected himself as the company's top star as World Champion, before Cena/Orton/Batista came to rise in WWE. After this, Triple H's ego grew greater.
But in all this time, he was carried by his opponents in the ring - mainly Shawn Michaels during their months-long epic feud on Raw. And even if he did carry his opponents on occasion, he didn't exactly have 5-star matches. And, you have to admit, he DID hold down some younger, deserving talents (albeit for a while) so he could push himself into more high-profile feuds, and brag in his promos of how he has beaten "everyone".
In his whole career, he has wormed his way to the top - and the whole time, he thought he one of the great wrestlers in WWE: from sucking up/carrying the bags to get into the "Kliq", to cheating on Chyna and seducing and marrying Stephanie, and pushing to "daddy-in-law" for him to stay World Champion for 2 years, on-and-off.
Triple H thinks he's great because he was boooked to look great, not because of his wrestling ability and earning his way up the ladder. 'Nuff said. (In my opinion)