I see Bowser as a selfish king who wants to beat Mario because he's a rival for Peach's heart. He kidnaps her just so Mario will come and he can get the chance to defeat him. But if need be, he will help Mario, especially if his ability to rule is threatened. But he wouldn't kill Mario even if he beat him, he'd probably lock him up or something (see: Super Princess Peach, he clearly overpowered Mario in that game and simply had him locked up. Also, in Paper Mario he beat Mario but just threw him out of the castle)
Bowser loves to get his way but he does have standards such as being disgusted by Count Bleck's intention of creating a world where nothing exists. Once the greater threat is gone, Bowser will go back to trying to beat Mario (see: Bowser's Inside Story) but he will go to great lengths to show off his ego and be a tough guy, and also does not want Peach to die. He held the ceiling up in SPM to A) show that he's tougher than O'Chunks and B) to make sure Peach isn't destroyed, because he's in love with her.
Also, Bowser loves to compete in more friendly competition with Mario and others, such as kart racing and sports. He's never invited to Mario Party because of his schemes against the Mushroom Kingdom so that is why he crashes the parties instead. Bowser Jr. and Kamek (and other Bowser minions) have been allowed in because they tricked Mario and Co into thinking they've reformed. Bowser doesn't do this because he enjoys crashing the parties instead. Bowser pays his minions to endure his attacks in those games. Mario Kart and Sports are hosted by someone unseen and unrelated to Mario and Co, so Mario doesn't get to decide whether Bowser is allowed in or not.
So basically Mario's rival who really doesn't need to be portrayed as a cruel merciless killer (though Galaxy and Dream Team pull this off really well) but instead is a staple of the series and a trouble maker.