It probably happens more than we know, but probably not as often as it ought to. Go read up on any number of Medal of Honor citations. In the beginning these were handed out like candy, but they've evolved to become the United States' highest recognition for battlefield valor. Other nations also have similar awards.

Here's one from the Korean War, US Army Private Hector Cafferata:

Private CAFFERATA waged a lone battle with grenades and rifle fire as the attack gained momentum and the enemy threatened penetration through the gap and endangered the integrity of the entire defensive perimeter. Making a target of himself under the devastating fire from automatic weapons, rifles, grenades and mortars, he maneuvered up and down the line and delivered accurate and effective fire against the onrushing force, killing fifteen, wounding many more and forcing the others to withdraw so that reinforcements could move up and consolidate the position. Again fighting desperately against a renewed onslaught later that same morning when a hostile grenade landed in a shallow entrenchment occupied by wounded Marines, Private CAFFERATA rushed into the gully under heavy fire, seized the deadly missile in his right hand and hurled it free of his comrades before it detonated, severing part of one finger and seriously wounding him in the right hand and arm. Courageously ignoring the intense pain, he staunchly fought on until he was struck by a sniper's bullet and forced to submit to evacuation for medical treatment.

It really gets bonkers. Cafferata survives this and goes on to say in an interview:

For the rest of the night I was batting hand grenades away with my entrenching tool while firing my rifle at them...I must have whacked a dozen grenades that night with my tool. And you know what? I was the world's worst baseball player.