What a god is kinda depends on the setting. Some settings it isn't possible, others it's mundane; in the Exalted and Planescape settings, minor gods can pop up with more frequency, and while tough are still killable, permanently (most other settings of D&D have gods being completely untouchable, but they aren't as common and don't show up personally).
So it really just depends on what defines a 'god' in the setting. This is of particular note in 4th ed D&D since there are basically paths to become literally god-like for player characters, meaning lesser gods are not an unrealistic challenge, nor an uncommon thing. In say, the Warhammer (and 40K) settings, the gods are very rare and are much more truly immortal and would be an unthinkable challenge; even the other gods likely couldn't kill one (as evidenced by the 4 Chaos gods so far being unable to slaughter Sigmar, which I'm sure they'd love to do).
So it really just depends on what defines a 'god' in the setting. This is of particular note in 4th ed D&D since there are basically paths to become literally god-like for player characters, meaning lesser gods are not an unrealistic challenge, nor an uncommon thing. In say, the Warhammer (and 40K) settings, the gods are very rare and are much more truly immortal and would be an unthinkable challenge; even the other gods likely couldn't kill one (as evidenced by the 4 Chaos gods so far being unable to slaughter Sigmar, which I'm sure they'd love to do).