Hand Grenades were used constantly in combat, and unlike in the movies, are a necessity both for offensive and defensive combat.

There are various mentions in WWII of 'Hand Grenade Duels' and sharp exchanges would often occur between infantry in urban, room to room and hill-side engagements. In one famous incident at Verrieres Ridge in Normandy, German and Canadian infantry engaged in a hand grenade duel within whispering distance of one another; as the Canadians occupied one side of a ridge, and the Germans the other.

The phrase 'grenade duel' seems to come up most often in scenarios of close fighting; such as the pacific.

Two excerpts from the MoH citations of Joseph Barry and Bill Foster, respectively -admittedly extraordinary circumstances, but the best I could get on short notice:

When infiltrating Japanese soldiers launched a surprise attack shortly after midnight in an attempt to overrun his position, he engaged in a pitched hand grenade duel, returning the dangerous weapons with prompt and deadly accuracy until an enemy grenade landed in the foxhole

The key thing to seize on here is that the Japanese both used them offensively, and that Barry used them defensively; often hurling the enemy's grenades back. He was awarded his medal posthumously.

Dug in with another Marine on the point of the perimeter defense after waging a furious assault against a strongly fortified Japanese position, Private First Class Foster and comrade engaged in a fierce hand grenade duel with infiltrating enemy soldiers.

More of the same. Once at close range, and in low visibility terrain, a hand grenade is more valuable than a rifle - hence their frequent use by infiltrating Japanese soldiers. Foster would smother a grenade with his body and be posthumously awarded his medal. Fortifications, fieldworks of even a minor nature, and perimeter defenses are all things that often need to be eliminated through maneuver; not just firepower. This means attackers have to get close, hence the primacy of grenades in these two excerpts.

These are perhaps two extraordinary circumstances, but if one reads enough AARs from enough unit histories the patterns I briefly pointed out here will show themselves time and again for the employment of hand-grenades throughout both World Wars. To be pointed; would you storm a trenchline and not use the most potent weapon given you? As usual, Hollywood gets it (mostly) wrong.