Ordinarily, no, except for the circumstances mentioned by the other users (if you suspect that they will switch to a faster Pokémon, debuff your Speed, or buff their own Speed to become faster than you; to increase the power of Electro Ball; to increase the power of Gyro Ball if Trick Room is in effect; or if you wish to transfer the buff to another Pokémon using Baton Pass).

It's impossible for a Pokémon (with the exception of Mega Kangaskhan) to attack twice in one turn. The only thing Speed is used for (apart from Electro Ball and Gyro Ball) is to see who goes first, and even then, it's only used if both Pokémon use moves with the same priority.

If both moves are of different priorities, the one with the higher priority always goes first, regardless of Speed stat. Otherwise, the faster Pokémon goes first (or the slower one if Trick Room is in effect).

HOWEVER, in the Generation I games (Red/Blue/Yellow/Stadium), speed is used to determine critical hit ratio. The faster you are, the more likely it is that you will get a critical hit. (This is not the case from Gold/Silver onwards)

Ordinarily, no, except for the circumstances mentioned by the other users (if you suspect that they will switch to a faster Pokémon, debuff your Speed, or buff their own Speed to become faster than you; to increase the power of Electro Ball; to increase the power of Gyro Ball if Trick Room is in effect; or if you wish to transfer the buff to another Pokémon using Baton Pass).

It's impossible for a Pokémon (with the exception of Mega Kangaskhan) to attack twice in one turn. The only thing Speed is used for (apart from Electro Ball and Gyro Ball) is to see who goes first, and even then, it's only used if both Pokémon use moves with the same priority.

If both moves are of different priorities, the one with the higher priority always goes first, regardless of Speed stat. Otherwise, the faster Pokémon goes first (or the slower one if Trick Room is in effect).