I get the emphasis on championships, but if we are going solely by Championships, then Will Perdue is better than Patrick Ewing. Basketball is a team game, and a lot of these players had incredible supporting casts, while others did not.
Assessing them solely on their ability as center:
1) Olajuwon - His stats were incredible, as was his longevity. Most impressive is that he did it with bad supporting casts. Other than a couple of years with a mercurial Ralph Sampson, and a couple of years with an over the hill Clyde Drexler, he never had a top player around him, yet won 2 championships, made another NBA finals, and went deep in the playoffs on multiple occasions. He did it in an era where there were many other top players.
One of the most impressive things about Olajuwon was how he dominated other top centers. He dominated David Robinson in the 1995 Eastern Conference Finals and outplayed Shaq in the 1995 NBA Finals, and he was 32 years old when he did that.
2) Wilt
3) Kareem - A great player that benefitted from playing on great teams. His first championship was with the Big O, and the rest of his titles were with Magic.
4) Shaq - even a fat Shaq that couldn't shoot free throws AT ALL dominated the NBA for almost his entire career.
5) Moses Malone - His stats are insane, and he played most of his career on bad teams. He took a bad Houston team to the NBA Finals in 1981, and got Dr. J his only title, turning Philly into a dominant team in 1983. He was as dominant in his era as just about any player at any position.
6) Bill Russell - He benefitted from playing on the dominant team of his era. I also think his stats are a bit of an issue compared to the other players on this list, especially for the era he played in. The 44% shooting percentage is the biggest problem. Still, he has a ton of titles and his defense and rebounding would be great for any era, so he belongs on this list, but he is not Top 5.
7) David Robinson - He is one of my favorite players of all time stylistically. He was in incredible shape and worked as hard as any player of any era. But he didn't have that killer instinct, often choked in big games, and needed Tim Duncan to win his only title.
8) Patrick Ewing - He needed one more quality teammate to win a title, and that teammate never came. Great player.
9) Bob Lanier - Dominated the 70's on mediocre Detroit teams, but he was great in his prime and would be great if he played today.
10) Dwight Howard - He is an odd duck and most players that have played with him hate him, but he has good stats and was dominant in his prime.
Others:
Dave Cowens - never a dominant player
Bill Walton - his prime was too short
Willis Reed - prime was too short
Robert Parish - never a top scorer