Shaq
The MVP (Most Valuable Player) is an award handed out during the NBA playoffs. Many people around the league (analysts, commentators, etc.) are allowed to vote for who they believe is the NBA MVP for the regular season. This is different from the NBA Finals' MVP. As of the 2008-2009 season, LeBron James is the last winner of the MVP trophy.
As near as I can tell from eye-balling/cross referencing a couple of websites, there has never been a situation where the team with the MVP on its roster did not make the playoffs.
Shaquille O'Neal was the MVP of the 2000 NBA Finals. His stats during the 2000 NBA playoffs were:30.7 PPG15.4 RPG3.1 APG2.4 BPG.566 FG%.456 FT%
In the 1978 NBA playoffs the Eastern Conference champion Washington Bullets defeated the Western Conference champion Seattle SuperSonics 4 games to 3. Wes Unseld was named NBA Finals MVP.
As of the 2008 playoffs, that was Tim Duncan of the San Antonio Spurs in 2003.
The San Antonio Spurs beat the Cleveland Cavaliers 4-0! Tony Parker was named Finals MVP!
Considering that their are only 4 given out for the entire season (Rookie Challenge MVP, All-Star Game MVP, NBA MVP [for the season], and the NBA Finals MVP), the most prestigious would easily be the NBA MVP award.
of course, If the player that is chosen did not make the playoffs, he will win the MVP award.
Kareem Abdul-Jabbar with 6 NBA MVP awards
No, he never won NBA MVP.