Yes, good IVs are extremely important in competitive battling. Good IVs can have an almost as big- or bigger impact on stats as Natures can. I was too lazy to breed my Primeape for perfect Attack (it only has an IV of 28 it in it) and thanks to that it has left many Pokémon with just 1 HP; something those 3 extra Attack points could have taken care of. Usually you'll want to aim for 29 - 31 in the 3 most important stats (for example Attack, Speed and HP for Garchomp) and around 20 and up in the less important stats. For completely useless stats (such as Attack for Blissey) the IVs don't really matter, but anything that could make a difference should be high-ish.