In the main Pokémon series, the Speed stat is used to determine which Pokémon attacks in what order. Generally, the faster Pokémon go first with the exception of Trick Room. Moves also have Priority which overrides the speed stat unless the Pokémon use moves with the same Priority. There is some variation within close speed stats so, sometimes the slower Pokémon goes first. Some moves rely on difference in speed stat for the damage calculation
In the Fire Emblem series, the Speed stat determines the number of attacks each fighter can make in an encounter. The general rule is that when a character exceeds the speed of their opponent by 5 (4 in early entries), they perform two attacks instead of one. Brave weapons can attack up to 4 times if they still have the speed over their opponent. Prior to Awakening, there was a speed penalty for not having enough constitution (strength in the Radiant saga) for their weapon that subtracted the speed for the difference. Fates streamlined the system so that certain weapons will have straight penalties listed on the item.
In some entries, the speed that plays a role in a character's evade stat.
In the various Mario role-playing games, the Speed stat tends to determine turn order with the fastest character going first with the others going in turn order. In Super Mario RPG, the speed stat can only increase with better gear. With the Mario & Luigi series, it is a standard stat that increases on level up. In Dream Team and Paper Jam, Speed Beans can permanently increase the stat with DX ones increasing by 3.