0 Attack IVs: Used for special attackers, so they don't take extra confusion and Foul Play damage.
0 Speed IVs: Used on slow Pokemon whose purpose is to go last (Payback, Trick Room, Gyro Ball).
0 Special Attack IVs: Almost completely useless, you don't need to worry about these at all.
0 HP, Defense, and Special Defense IVs: For Focus Sash users that need to go down to their Sash to be better (Unburden Sceptile, Acrobatics Ninjask, etc.)
As Chickenboy2004 said, in games where Hidden Power exists, a certain combination of IVs is needed to obtain the desired Hidden Power type.
There's also some extremely niche strategies that use things like Guard Split and Power Swap, meaning you may want a specific amount of IVs, but these are so bad they're never used.
The only common ones are 0 Attack and 0 Speed IVs, the rest you can do without.
Hope I helped!
